The contents uf t h 1 >
ia part without tpei
letin shall not M
authorization of
the Aeronautical Board*
ANC— 18
June, 1944
ANC BULLETIN
DESIGN OF WOOD
AIRCRAFT STRUCTURES
WAR DEPARTMENT
ARMY AIR FORCES
NAVY DEPARTMENT
BUREAU OF AERONAUTICS
DEPARTMENT OF COMMERCE
CIVIL AERONAUTICS ADMINISTRATION
Issued by the
ARMYNAVYCIVIL COMMITTEE
» on
AIRCRAFT DESIGN CRITERIA
Under the supervision of the
AERONAUTICAL BOARD
The contents of this bulletin shall not be reproduced in whole or
in part without specific authorization of the Aeronautical Board.
UNITED STATES GOVERNMENT PRINTING OFFICE
WASHINGTON: 1944
This Bulletin
by
FOREST PRODUCTS LABORATORY
FOREST SERVICE
UNITED STATES DEPARTMENT OF AGRICULTURE
and
ARMYNAVYCIVIL COMMITTEE
on
AIRCRAFT DESIGN CRITERIA
I]
NOTICE
The reader is hereby notified that this bulletin is subject to revision and amend
ment when and where such revision or amendment is necessary to effect
agreement with the latest approved information on aircraft design criteria.
When using this bulletin, the reader should therefore make certain that it is
the latest revision and that all issued amendments, if any, are known.
Ill
TABLE OF CONTENTS
Page
CHAPTER 1. GENERAL 1
1.0. Purpose and Use of Bulletin 1
1.1. Nomenclature , 1
CHAPTER 2. STRENGTH OF WOOD AND PLYWOOD ELEMENTS 9
2.0. Physical Characteristics of Wood 13
2.1. Basic Strength and Elastic Properties of Wood . . , 16
2.2. Columns 28
2.3. Beams 30
2.4. Torsion 36
2.5. Basic Strength and Elastic Properties of Plywood 37
2.6. Plywood Structural Elements 59
2.7. Flat Rectangular Plywood Panels 76
2.8. Curved Plywood Panels 109
2.9. Joints 114
CHAPTER 3. METHODS OF STRUCTURAL ANALYSIS 131
3.0. General 133
3.1. Wings 135
3.2. Fixed Tail Surfaces 185
3.3. Movable Control Surfaces 185
3.4. Fuselages 185
3.5. Hulls and Floats • 199
3.6. Miscellaneous 201
CHAPTER 4. DETAIL STRUCTURAL DESIGN 204
4.0. General 205
4.1. Plywood Covering 205
4.2. Beams 210
4.3. Ribs 216
4.4. Frames and Bulkheads 220
4.5. Stiffeners 220
4.6. Glue Joints 222
4.7. Mechanical Joints 224
4.8. Miscellaneous Design Details 227
4.9. Examples of Actual Design Details 233
IV
CHAPTER 1. GENERAL
1.0. PURPOSE AND USE OF BULLETIN.
1.00. Introduction. This bulletin has been prepared for use in the design of both
military and commercial aircraft, and contains material which is acceptable to the Army
Air Forces, Navy Bureau of Aeronautics, and the Civil Aeronautics Administration.
It should, of course, be understood that methods and procedures other than those out
lined herein are also acceptable, provided they are properly substantiated and approved
by the appropriate agency. The applicability and interpretation of the provisions of
this bulletin as contract or certification requirements will in each case be defined
by the procuring or certificating agency.
1.01. Scope of Bulletin. The technical material in this bulletin is contained in
chapters 2, 3, and 4, and pertains to three related phases of the structural design of
wood aircraft.
Chapter 2 presents information on the strength and elastic properties of structural
elements constructed of wood and plywood. This information supersedes that contained
in the October 1940 edition of ANC5, "Strength of Aircraft Elements."
Those sections of chapter 2, which are based on incomplete data or theoretical
analysis, that have not been fully verified by test have been, as a caution, marked with
a double asterisk. Those sections that are based on reasonably complete information
but require further substantiating tests are marked with a single asterisk. The use of
the various formulas and data in these sections should, therefore, be commensurate
with the limitations noted. Since further research on the strength and elastic properties
of wood and plywood structural elements is being actively carried on by the Forest
Products Laboratory, it is anticipated that revisions to chapter 2 will be made from
time to time as this work progresses.
Chapter 3 contains suggested methods of structural analysis for the design of various
aircraft components. Although these methods are in many cases the same as those
used for metal structures, special considerations have been introduced which take into
account the orthotropic properties of wood.
Chapter 4 presents recommendations on the detail structural design of wood air
craft and contains some examples of how various manufacturers have treated the solu
tion of specific detail design problems.
1.02. Acknowledgement. The ANC Committee on Aircraft Design Criteria and
the Forest Products Laboratory express their appreciation to aircraft manufacturers
and others for the valuable assistance given in connection with various parts of this
bulletin.
1.1. NOMENCLATURE.This section presents the definitions of standard structural
symbols which are used in the bulletin. In addition, sections 1.10 and 1.11 are presented
to clarify the differentiation between the definitions for strength and elastic properties
of plywood elements and those for like properties of plywood panels. These sections
also outline the use of table 29.
1
2
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
1.10. Definitions for Plywood Elements — Beams, Prisms and Columns in Com
pression, Strips in Tension. A plywood element is any rectangular piece of plywood
that is supported, loaded, or restrained on two opposite edges only. In defining the
various strength and elastic property terms for plywood elements; the face grain direc
tion has been used as a reference; for example, the subscript w denotes a direction
parallel to (with) the face grain, while the subscript x denotes a direction perpendicular
to (across) the face grain. This is illustrated by figure 11. The strength and elastic
properties given in table 29 of the bulletin are for plywood elements.
Figure 11. — Plywood element (supported, loaded, or restrained on two opposite edges only).
1.11. Definitions for Plywood Panels 1 . A plywood panel is any rectangular piece
of plywood that is supported, loaded, or restrained on more than two edges. In defining
the various strength and related property terms for plywood panels, the side of length a
rather than the face grain direction has been used as the reference. For any panel having
tension or compression loads (either alone or accompanied by shear) the side of length a
is the loaded side. For panels having only shear loads (with no tension or compression),
the side a may be taken as either side. (Sec. 2.701). For panels having normal loads,
side a is the shorter side. The subscripts a and 1 denote a direction parallel to the side
of length a, and the subscripts b and 2 denote a direction perpendicular to the side of
length a. This is illustrated by figure 12. Since, in panels, the directions in which
E a , E b , Ei, E 2 , etc., are to be measured are related to the directions of the sides of lengths
a and b, it is necessary to relate these directions to the face grain direction before the
terms can be evaluated from table 29. It may be stated, therefore, that:
TABLE Z3
TABLE 29
b
E a . E f , ETC— CANNOT BE L E i) ,E 2 , ETC— CANNOT BE
EVALUATED UNTIL EACE EVALUATED UNTIL FACE
GRAIN DIRECTION 15 KNOWN GRAIN DIRECTION 15 If NO INN
Figure 12. — Plywood panel (supported, loaded, or restrained on more than two edges).
1 The designations for sides a and b as used herein are different from those used in ANC5, in which
the side of length h is defined as the loaded side in tension or compression and as the short side in shear
GENERAL
3
( 1 ) When the face grain direction of a plywood panel is parallel to the side of length
a, the values of E a , E h , E h E>, etc, may be taken from the columns for E w , E T , E fw , E fx ,
etc., respectively, in table 2 9. This is illustrated by figure 13.
E^.E,, ETC. VALUES FROM
COLUMNS FOR E Wt E fw ,ETC.
E^ ETC. VALUES FROM
COLUMNS FOR E Xt E fx ,ETC. }
RES PEC TI VEL Y t IN TABLE RE5PECTIVEL Y, IN TABLE
Z9 29
Figure 13. — Plywood panel (face grain direction parallel to side of length a).
(2) When the face grain direction of a plywood panel is perpendicular to the side
of length a, the values of E a , E b , E,, Eg, etc., may be taken from the' columns for E x ,
E w , E fx , E fw , etc., respectively, in table 29. This is illustrated by figure 14.
T
a
1
////////////////// //////////
FACE GRAIN
' DIRECTION
V77777777,
E„ E ETCVALUES FROM
7Z
E b ,E z> ETC VALUES FROM
COL UMAI5 FOR E x , E fx , ETC, COL UMNS E„ t E fw ,ETC,
RESPECTIVELY, IN TABLE RESPECTIVELY, 7n TABLE
2.3 29
Figure 14. — Plywood panel (face grain direction perpendicular to side of length a).
1.12. STANDARD STRUCTURAL SYMBOLS FOR CHAPTER TWO. In
general, symbols that are used only in the section where they are defined are not included
in this nomenclature. »
area of cross section, square inches
(total).
area of plies with grain direction parallel
to the direction of applied stress.
The length of the loaded side of a ply
wood panel for compression or tension
loads, and the length of either side for
shear loads (Sec. 2.701); subscript de
noting parallel to side of length a for
plywood panels.
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
area of plies with grain direction per
pendicular to the direction of applied
stress (surfaces of plies parallel to plane
of glue joint tangential to the annual
growth rings, as for rotarycut or flat
sliced veneer, flatsawn lumber).
area of plies with grain direction per
pendicular to the direction of applied
stress (surfaces of plies parallel to plane
of glue joint radial to the annual growth
rings, as for quartersliced veneer,
quartersawn lumber).
circumference
diameter
modulus of elasticity of wood in the
direction parallel to the grain, as de
termined from a static, bending test.
(This value is listed in table 24.)
modulus of elasticity of wood in the
direction radial to the annual growth
rings.
modulus of elasticity of wood in the
direction tangential to the annual growth
rings.
modulus of elasticity of wood in the
direction parallel to the grain, as de
termined from a compression test
(value not listed in table 24, but ap
proximately equal to 1.1 El).
effective modulus of elasticity of ply
wood in tension or compression measured
parallel to the side of length a of ply
wood panels.
b — the length of the unloaded side of a ply
wood panel for compression or tension
loads, and the length of either side for
shear loads (Sec. 2.701); subscript de
noting parallel to side of length b for
plywood panels; subscript denoting
"bending" for solid wood.
br — subscript denoting "bearing."
c — endfixity coefficient for columns; sub
script denoting "compression '; distance
from neutral axis to extreme fiber.
c' — distance fr om neutral axis to the extreme
fiber having grain direction parallel to
the applied stress (plywood).
cr — subscript denoting "critical."
d —depth or height
cz, — unit strain (tension or compression) in
the L direction.
cr — unit strain (tension or compression) in
the R direction.
ct — unit strain (tension or compression) in
the T direction.
(Lit
unit strain (shear) or the change in
angle between lines originally drawn in
the L and T directions,
unit strain (shear) or the change in
angle between lines originally drawn in
t he L and R directions,
unit strain (shear) or the change in
angle between lines originally drawn in
the T and R directions.
GENERAL
5
Eb — effective modulus of elasticity of ply
wood in tension or compression measured
perpendicular to the side of length a of
plywood panels.
E w — effective modulus of elasticity of ply
wood in tension or compression measured
parallel to (with) the grain direction of
the face plies.
E x — effective modulus of elasticity of ply
wood in tension or compression measured
perpendicular to (across) the grain <li
rection of the face plies.
Ef W — effective modulus of elasticity of ply
wood in flexure (bending) measured
parallel to (with) the grain direction of
the face plies.
E fx — effective modulus of elasticity of ply
wood in flexure (bending) measured per
pendicular to (across) the grain direction
of the face plies.
E' f X — same as Ef X , except that outermost ply
on tension side is neglected (not to he
used in deflection formulas).
E\ — effective modulus of elasticity of ply
wood in flexure (bending) measured
parallel to the side of length a of ply
wood panels.
Ei — effective modulus of elasticity of ply
wood in flexure (bending) measured per
pendicular to the side of length a of
plywood panels.
F — allowable stress; stress determined from
test.
Fb — allowable bending stress.
/''(,„ — modulus of rupture in bending for solid
wood parallel to grain.
Fb P — fiber stress at proportional limit in bend
ing for solid wood parallel to grain.
Fbrp — bearing stress at proportional limit
parallel to the grain for solid wood.
Fbrr — allowable ultimate bearing stress per
pendicular to grain for solid wood (either
radial or tangential to the annual growth
rings).
Fbru — allowable ultimate bearing stress parallel
to grain.
/ — internal (or calculated) stress; subscript
denoting "flexure" (bending) for ply
wood.
fb — internal (or calculated) primary bend
ing stress.
fbr — internal (or calculated) bearing stress
i
6 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
— allowable compressive stress.
— critical compressive stress for the
buckling of rectangular plywood panels.
/„ — internal (or calculated) compressive
stress.
jcL — internal (or calculated) compressive
stress in a longitudinal ply; i.e., any
ply with its grain direction parallel to
the applied stress.
F C p — stress at proportional limit in compres
sion parallel to grain for solid wood.
F cp T — stress at proportional limit in com
pression perpendicular to grain for solid
wood (either radial or tangential to the
annual growth rings).
Fcpw — stress at proportional limit in compres
sion for plywood having the face grain
direction parallel to {with) the applied
stress.
F CP x — stress at proportional limit in com
pression for plywood having the face
grain direction perpendicular to (across)
the applied stress.
F,,,e — stress at proportional limit in com
pression for plywood having the face
grain direction at an angle 6 to the
applied stress.
F cu —ultimate compressive stress parallel to \
the grain for solid wood.
F cuT — compressive strength perpendicular to
grain for solid wood (either radial or
tangential to the annual growth rings).
Taken as 1 .33 times F cp t
Fcnw — ultimate compressive stress for ply
wood having the face grain direction
parallel to (with) the applied stress.
F ruI — ultimate compressive stress for plywood
having the face grain direction perpen
dicular to (across) the applied stress.
FcuO — ultimate compressive stress for plywood
having the face grain direction at an
angle 6 to the applied stress.
F s — allowable shearing stress. V — internal (or calculated) shearing stress.
F Scr — critical shear stress for the buckling of
rectangular plywood panels.
F st — modulus of rupture in torsion.
F S u — ultimate shear stress parallel to grain
for solid wood.
F s d c — untimate shear stress for plywood,
wherein 6 designates the angle between
the face grain direction and the shear
stress in a plywood element so loaded in
shear that the face grain is stressed in
compression.
c
GENERAL
7
F s 8t — ultimate shear stress for plywood,
wherein 6 designates the angle between
the face grain direction and the shear
stress in a plywood element so loaded
in shear that the face grain is stressed
in tension.
F swx — ultimate shear stress for plywood ele
ments for the case where the face grain
is at 0° and 90° to the shear stress.
Ft —allowable tension stress.
ft — internal (or calculated) tensile stress.
f t L — internal (or calculated) tensile stress in
a longitudinal ply (any ply with its
grain direction parallel to the applied
stress).
Ftu — ultimate tensile stress parallel to grain
for solid wood.
F tU T — tensile strength perpendicular to grain
for solid wood (either radial or tan
gential to the annual growth rings).
F lU w — ultimate tensile stress for plywood hav
ing the face grain direction parallel to
(with) the applied stress.
F tux — ultimate tensile stress for plywood
having the face grain direction perpen
dicular to (across) the applied stress.
FtuB — ultimate tensile stress for plywood hav
ing the face grain direction at an angle
6 to the applied stress.
G — mean modulus of rigidity taken as 1/16
of E L .
Gl,t — modulus of rigidity associated with shear
deformations in the LT plane resulting
from shear stresses in the LR and RT
planes.
Glr — modulus of rigidity associated with shear
deformations in the LR plane resulting
from shear stresses in the LT and RT
planes.
Gj r — modulus ot rigidity associated with shear
deformations in the TR plane resulting
from shear stresses in the LT and LR
planes.
H —
I — moment of inertia.
1 P — polar moment of inertia.
,/ — Torsion constant (I p for round tubes).
A" — a constant, generally empirical.
L — length; span; subscript denoting the
direction parallel to the grain.
L
L' = —where c is the end fixity coefficient.
V c
M — applied bending moment.
N —
h — height or depth.
i — subscript denoting "ith ply."
j — stiffness factor \/EI/P
k —
I — not used, to avoid confusion with the
numeral 1.
in —
n — number of plies.
8
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
P — applied load (total, not unit load).
(J — static moment of a cross section.
R — subscript denoting the direction radial
to the annual growth rings and per
pendicular to the grain direction.
S — shear force.
T — applied torsional moment, torque; sub
script denoting the direction tangential
to the annual growth rings and per
pendicular to the grain direction.
U
w —
Z — section modulus, I/c
Z,, — polar section modulus, I p /c.
* — a single asterisk after a section number
indicates that the section is based on
resonably complete information but re
quires further substantiating tests.
** — double asterisks indicate sections, based
on incomplete data or theoretical an
alysis, that have not been fully verified
by test.
l> — subscript denoting "polar"; subscript
denoting "proportional limit"; load per
unit area.
psi — pounds per square inch.
q — shear flow, pounds per inch.
r —radius.
s — subscript denoting "shear."
t — thickness; subscript denoting "tension."
i, — thickness of central ply.
tj — thickness of face ply.
u — subscript denoting "ultimate."
w — deflection of plywood panels; load per
linear inch; subscript denoting parallel
to face grain ot plywood.
x subscript denoting perpendicular to face
grain of plywood.
?/ — distance from the neutral axis to any
given fiber.
2
(i — the angle between side of length b and
the face grain direction as used in
the determination of buckling criteria
for panels (Sec. 2.70).
— deflection.
— usually the acute angle in degrees be
tween the face grain direction and the
direction of the applied stress; angle
of twist in radians in a length (L).
Illt — Poisson's ratio of contraction along the
direction T to extension along the
direction L due to a normal tensile
stress on the RT plane; similarly, [llrj
VKT, VTR, VIiL, and \kTL
p — radius of gyration.
4> — usually the acute angle in degrees be
tween the face grain direction and the
axis of extension.
CHAPTER 2. STRENGTH OF WOOD AND PLYWOOD ELEMENTS
TABLE OF CONTENTS
2.0. PHYSICAL CHARACTERISTICS
OF WOOD 13
2.00. Anisotropy of Wood 13
2.01. Density or Apparent Specific
Gravity 15
2.02. Moisture Content 15
2.03. Shrinkage Hi
2.1. BASIC STRENGTH AND ELAS
TIC PROPERTIES OF
WOOD 16
2.10. Design Values, Table 23 16
2.100. Supplemental Notes 21
2.1000. Compression Perpendicular to
Grain 21
2.1001. Compression Parallel to Grain . 21
2.11. Notes on the Use of Values
in Table 23 21
*2.110. Relation of Design Values in
Table 23 to Slope of Grain . . 21
2.111. Tension Parallel to Grain 21
2.112. Tension Perpendicular to
Grain 22
2.12. Standard Test Procedures. 22
2.120. Static Bending 22
2.1200. Modulus of Elasticity (E L ) ... 22
2.1201. Fiber Stress at Proportional
Limit (F bp ) 24
2.1202. Modulus of Rupture (F bll ) 24
2.1203. Work to Maximum Load 24
2.121. Compression Parallel to Grain . 24
2.1210. Modulus of Elasticity (E Lc ) ... . 24
2.1211. Fiber Stress at Proportional
Limit (F cp ) 25
2.1212. Maximum Crushing Strength
(F cu ) 25
2.122. Compression Perpendicular to
Grain 25
2.123. Shear Parallel to Grain (F sv ) ... 25
2.124. Hardness 27
2.125. Tension Perpendicular to
Grain (F tuT ) 27
2.13. Elastic Properties Not In
cluded in Table 23 27
2.130. Moduli of Elasticity Perpen
dicular to Grain (E T , Er). . . . 27
•2.131. Moduli of Rigidity (Glt, Glr,
G bt ) 27
*2.132. Poisson's Ratios ([/.) 28
2.14. StressStrain Relations 28
2.2. COLUMNS 28
2.20. Primary Failure 28
2.21. Local Buckling and Twisting
Failure 28
2.22. Lateral Buckling 23
2.3. BEAMS 30
2.30. Form Factors 30
2.31. Torsional Instability 32
2.32. Combined Loadings 32
2.320. General 32
2.321. Bending and Compression 32
2.322. Bending and Tension 34
2.33. Shear Webs 34
2.34. Beam Section Efficiency 34
2.4. TORSION 36
2.40. General 36
2.41. Torsional Properties 36
2.5. BASIC STRENGTH AND ELASTIC
PROPERTIES OF PLY
WOOD 37
2.50. General 37
2.51. Analysis of Plywood Strength
Properties (General) 38
2.52. Basic Formulas 39
*2.53. Approximate Methods for
Calculating Plywood
Strengths 42
2.54. MoistureStrength Relations
for Plywood 42
2.540. General " 42
2.541. Approximate Methods for
Making Moisture Correc
tions for Plywood Strength
Properties 42
2.5410. Moisture Corrections for Ply
wood Compressive Strength
(0° or 90° to Face Grain Di
rection) 43
*2.5411. Moisture Corrections for Ply
wood Tensile Strength (0° or
90° to Face Grain Direction). 43
*2.5412. Moisture Corrections for Ply
wood Shear Strength (0° or
90° to Face Grain Direction). 43
2.5413. Moisture Corrections for Ply
wood Compressive Strength
(Any Angle to Face Grain
Direction) 43
9
10
2.5414. Moisture Corrections for Ply
wood Tensile Strength (Any
AngletoFace Grain Direction) . 43
2.5415. Moisture Corrections for Ply
wood Shear Strength (Any
Angleto Face Grain Direction ) 43
2.55. Specific Gravity Strength Re
lations for Plywood 43
2.56. StressStrain Relations for
Wood and Plywood 45
2.560. Derivation of General Stress
Strain Relations for Plywood. . . 46
2.5600. Obtaining Strains from
Given Stresses 46
2.5601. Obtaining Stresses from
Given Strains 46
2.561. StressStrain Relations for
Specific Cases 49
*2.5610. Stress and Strain Circle Con
stants 49
2.5611. StressStrain Relations in
45° Plywood 54
2.56110. Tension at 45° to the Face
Grain 55
2.56111. Shear at 45° to the Face
Grain 57
*2. 56112. Experimental Stress Strain
Data 59
2.6. PLYWOOD STRUCTURAL ELE
MENTS 59
2.60. Elements (0 =0° or 90°) 59
2.600. Elements in Compression
(6=0° or 90°) 59
*2.601. Elements in Tension
(8=0° or90°) 61
*2.602. Elements in Shear
(8 =9° or 90°).... 61
2.61. Elements (8 = Any Angle) 61
*2.610. Elements in Compression
(6 = Any Angle) 61
2.61 1 . Elements in Tension
(8 = Any Angle) 62
*2.612. Elements in Shear
(8 = Any Angle) 62
*2.613. Elements in Combined Com
pression (or Tension) and
Shear (6 = Any Angle) 63
2.614. Elements in Bending 64
**2.6140. Deflections 65
*2.615. Elements as Columns 65
2.7. FLAT RECTANGULAR PLY
WOOD PANELS 76
2.70. Buckling Criteria 76
2.71. General 76
*2.710. Compression or Shear . 7G
**2.711. Combined Compression (of
Tension) and Shear Panel
Edges Simply Supported 77
2.72. Allowable Shear in Plywood
Webs 96
2.720. General ' 96
*2.721. Allowable Shear Stresses 96
2.722. Use of Figure 241 97
*2.723. Buckling of Plywood Shear
Webs 100
2.73. Lightening Holes ' 100
*2.74. Torsional Strength and
Rigidity of Box Spars 100
2.75. Plywood Panels Under Nor
mal Loads 100
2.750. General 100
2.751. Small Deflections 100
2.752. Large Deflections 103
2.76. Stiffened Flat Plywood Panels 103
*2.760. Effective Widths in Com
pression 103
*2.761. Compressive Strength 105
*2.7610. Modes of Failure in Stiffened
Panels 107
*2.762. Bending 107
2.8. CURVED PLYWOOD PANELS. ... 109
**2.80. Buckling in Compression 109
*2.81. Strength in Compression or
Shear: or Combined Com
pression (or Tension) and
Shear 109
2.82. Circular ThinWalled Ply
wood Cylinders 109
2.820. Compression with Face Grain
Parallel or Perpendicular to
the Axis of the Cylinder. . . . 109
*2.821. Compression with 45° Face
Grain. Ill
2.822. Bending Ill
*2.823. Torsion .' Ill
2.824. Combined Torsion and
Bending Ill
2.9. JOINTS 114
2.90. Bolted Joints 114
2.900. Bearing Parallel and Perpen
dicular to Grain 114
2.901. Bearing at an Angle to the
Grain 115
2.902. Bearing in Woods other than
Spruce 118
2.903. Combined Concentric and
Eccentric Loadings; Bolt
Groups 118
2.904. Bolt Spacings 118
11
2.9040. Spacing of Bolts Loaded
Parallel to the Grain 119
2.9041. Spacing of Bolts Loaded
Perpendicular to the Grain. . 119
2.9042. Spacing of Bolts Loaded at
an Angle to the Grain 119
2.9043. General Notes on Bolt Spacing. 119
2.905. Effects of Reinforcing Plates . . 121
2.900. Bushings 121
2.907. Hollow Bolts 121
2.908. Bearing in Plywood 122
2.91. Glued Joints 122
2.910. Allowable Stress for Glued
Joints 122
2.911. Laminated and Spliced Spars
and Spar Flanges 1 22
2.912. Glue Stress Between Wel>
and Flange 122
2.92. Properties of Modified
Wood 122
2.920. Detailed Test Data for
Tables 213 and 214 123
2.93. References 129
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
2.0. PHYSICAL CHARACTERISTICS OF WOOD.
2.00. Anisotropy of Wood. Wood, unlike most other commonly used structural
materials, is not isotropic. It is a complex structural material, consisting essentially
of fibers of cellulose cemented together by lignin. It is the shape, size, and arrangement
of these fibers, together with their physical and chemical composition that govern the
strength of wood, and account for the large difference in properties along and across
the grain.
The fibers are long and hollow tubes tapering toward the ends, which are closed.
Besides these vertical fibers, which are oriented with their longer dimension lengthwise
L
Figure 21.— Wood cellular structure. Drawing cf a highly magnified block of softwood measuring
about onefortieth inch vertically: it, transverse surface; rr, radial surface; tg, tangential surface; ar,
annual rings; urn, summerwood; sp, springwood; tr, tracheids, or fibers; hrd, horizontal resin duct;
far, fusiform wood ray; wr, wood rays; L, direction (longitudinal) of grain; R, direction radial to annual
rings and perpendicular to grain direction; T, direction tangential to annual rings and perpendicular
to grain direction; vrd, vertical resin duct.
13
14
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
of the tree and comprise the principal part of what is called wood, all species, except
palms and yuccas, contain horizontal strips of cells known as rays, which are oriented
radially and are an important part of the tree's food transfer and storage system. Among
different species the rays differ widely in their size and prevalence.
From the strength standpoint, this arrangement of fibers results in an anisotropic
structure, that accounts for three Young's moduli differing by as much as 150 to 1, three
shear moduli differing by as much as 20 to 1, six Poisson's ratios differing by as much as
40 to 1, and other properties differing by various amounts. Not all of these wood
properties have, as yet, been thoroughly evaluated.
Figure 21 shows a diagrammatic sketch of the cellular structure of wood. Each
year's growth is represented by one annual ring. The portion of the growth occurring
in the spring consists of relatively thinwalled fibers, while that occurring during 'the
later portion of the growing season consists of fibers having somewhat heavier walls.
Thus, there is, for most woods, a definite line of demarcation between the growth
occurring in successive years. The relation between the cellular structure of the wood
and the three principal axes — longitudinal (L), tangential (T), and radial (R) — is indi
cated on the sketch. Figure 22 shows the relation between these axes and (a) the log,
ra) LOO
C6) POTJ/?V C(/r l/£/V££/? OS? ££/!£ S4t*W /.VA/S£/?
L
Cc) Q(/A/?T£& 5l/C££ l/£W££P O/? ££&£ 0/?4 /A/ L(JMg£/?
Figx t re 22. — Principal directions in wood and plywood.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
15
(b) a flatsawn board or rotarycut veneer, and (c) an edgegrain board or quarter
sliced veneer.
Table 21 — Variation oj wood strength properties with specific gravity 1
i or
S = strength at specific gravity g
.s" = strength at specific, gravity g'
(usually average values from
column (2) of table 23).
Static bending:
Fiber stress at proportional limit
Modulus of rupture
Modulus of elasticity
Work to maximum load
Total work
Impact bending:
Fiber stress at proportional limit
Modulus of elasticity
Height of drop
1 Values in this table apply only to variations within a species. See section 2.'
1.50
1.50
1.25
2.00
2.25
1.50
1.25
2.00
Compression parallel to grain:
Fiber stress at proportional limit
Maximum crushing strength ....
Modulus of elasticity
Compression perpendicular to grain:
Fiber stress at proportional limit
Hardness — end, radial, tangential. . . .
1.25
1.25
1.25
2.50
2.50
2.01. Density or Apparent Specific Gravity. The substance of which wood is com
posed is actually heavier than water, its specific gravity being nearly the same for all
species and averaging about 1.5. Since a certain proportion of the volume of wood is
occupied by cell cavities, the apparent specific gravity of the wood of most species is
less than unity.
Relations between various strength properties and specific gravity have been
developed (table 21) and are useful in estimating the strength of a piece of wood of
known specific gravity. Considerable variability from these general relations is found,
so that while they cannot be expected to give exact strength values, they do give good
estimates of strength. Minimum permissible specific gravity values are listed in section
2.10.
The exponential values shown in table 21 apply to variation within a species.
That is, they are to be used in determining the relation between the strength properties
of pieces of the same species but of different specific gravity. For expressing the relation
between the average strength properties of different species, the exponential values are
somewhat lower. Such values are shown in table 14 of U. S. Department of Agriculture
Technical Bulletin 479 (ref. 217).
2.02. Moisture Content. Wood in the natural state in the living tree has con
siderable water associated with it. After being converted to lumber or other usable
form, or during conversion, wood is commonly dried so that most of the water is removed.
The water is associated with the wood in two ways, either absorbed in the cell walls,
or as free water in the cell cavities. During drying, the free .water in the cell cavities
16
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
is removed first, then that absorbed in the cell walls. The point at which all the water
has been removed from the cell cavities while the cell walls remain saturated is known as
the fibersaturation point. For most species, the moisture content at fiber saturation
is from 22 to 30 percent of the weight of the dry wood.
Lowering the moisture content to the fibersaturation point results in no changes
in dimension or in strength properties. Lowering the moisture content below the fiber
saturation point, however, results in shrinkage and an increase in strength properties.
Wood is a hygroscopic material, continually giving off or taking on moisture in
accordance with the relative humidity and temperature to which it is exposed. Thus,
while the strength of a piece of wood may be increased to a relatively high value by
drying to a low moisture content, some of that increase may be lost if, in use, it is ex
posed to atmospheric conditions that tend to increase the moisture content. While
paint and other coatings may be employed to retard the rate of absorption of moisture
by wood, they do not change its hygroscopic properties, thus a piece of wood may be
expected to come to the same moisture content under the same exposure conditions
whether painted or unpainted. The time required will vary, depending upon whether
or not it is coated. It is desirable, therefore, to design a structure on the basis of the
strength corresponding to the conditions of use.
Moisture content is generally expressed as a percentage of the dry weight of the
wood. The percentage variation of wood strength properties for 1 percent change in
moisture content is given in table 22. Since this variation is an exponential function,
it is necessary that strength adjustments based on the percentage changes given in the
table be made successively for each 1 percent change in moisture content until the total
change has been covered.
2.03. Shrinkage. Reduction of moisture content below the fibersaturation point
results in a change in dimension of the wood. Shrinkage in the longitudinal direction
is generally negligible, but in the other two directions it is considerable. In general,
radial shrinkage is less than tangential, the ratio between the two varying with the
species.
A quartersawed board will, therefore, shrink less in width but more in thickness
than a flatsawed board. The smaller the ratio of radial to tangential shrinkage, the
more advantage is to be gained through minimizing shrinkage in width by using a quarter
sawed board. The smaller the difference between radial and tangential shrinkage, the
less, ordinarily, is the tendency to check in drying and to cup with changes in moisture
content.
In general, woods of high specific gravity shrink and swell more for a given change
in moisture content than do woods of low specific gravity.
2.1. BASIC STRENGTH AND ELASTIC PROPERTIES OF WOOD.
2.10. Design Values, Table 23. Strength properties of various species for use in
calculating the strength of aircraft elements are presented in table 23. Their applica
bility to the purpose is considered to have been substantiated by experience. The as
sumptions (see footnotes to table 23), made in deriving the values in table 23 from the
results of standard tests (sec. 2.12) particularly that relating to "duration of stress",
are, however, being reexamined in the light of recent data and additional studies are
under way to further clarify the basis of design. Included is experimental work to further
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
17
Table 22. — Percentage increase (or decrease) in wood strength properties for one percent decrease
(or increase) in moisture content 1
Static bending
Com
pres
sion
Com
Shear
parallel
pres
ing
Fiber
Mod
Mod
Work
to
sion
strength
Hard
Species
stress
ulus
ulus
to
grain,
perpen
parallel
ness
at pro
of
of
maxi
maxi
dicular
to
(side)
por
rup
elas
mum
mum
to
grain
tional
ture
ticity
load 2
crushing
grain
limit
strength
(1)
(2)
(3)
(4)
(5)
(6)
_
(7 )
(o)
( ■' )
H ardwoods: 3
8.9
0.4
3.6
1.8
8.3
6.8
5.1
4.1
4.1
3 5
1 4
.4
4.7
4.8
2.9
2.4
Basswood, American
6.8
"i.O
9 O
2.6
6.5
6.6
4.2
4.2
Beech, American
6.0
4 7
1 R
1 .0
2.0
6.2
5.3
3.8
3.6
6.4
o.u
9 Q
1.2
7.1
7.2
5.0
3.6
6.0
4.8
2.0
1.7
6.1
5.6
3.6
3.3
Cherry, black
6.6
3.6
1.1
1.0
6.0
5.5
3.5
3.1
Cottonwood
5.8
4.1
2.5
.1
6.6
5.7
2.6
1.8
Elm rock
4.7
3.8
2. 1
 .3
5.3
6.1
3.5
2.8
Hickory (true hickories)
4.9
4.8
2.8
 .7
5.9
6.6
3.9
Khava ("African mahogany")
3.2
2.5
1.6
 .G
3.2
3.0
.4
3.1
Mahogany
2.6
1.3
.8
2.9
2.5
3.9
1..
Maple, sugar
5.2
4.4
1 .4
1.9
5.7
7.1
3.9
3.4
Oak, commercial white ami red ....
4.6
4.4
2.4
1.7
5.9
4.4
3.5
1.8
Sweetgum .
6.7
4.7
2.2
1.5
6.1
5.4
3.5
2.4
5.8
3.7
1.4
2.6
4.8
6.3
1.0
1.0
Yellowpoplar
5.0
4.6
2.7
1.9
6.7
4.8
3.3
2.4
Softwoods (conifers) ^
4.6
4.0
1.6
1.8
4.9
5.1
1.7
2.3
4.5
3.7
1.8
1.9
5.5
5.0
1.7
2.9
Fir, noble
5.1
4.7
1.9
3.2
6.1
5.5
2.3
3.1
Hemlock, western
4.7
3.4
1.4
.7
5.0
3.7
2.5
2.0
3.4
2.1
1.8
1.4
4.3
4.0
.4
1.5
Pine, eastern white
5.6
4.8
2.0
2.1
5.7
5.6
2.2
2.2
Pine, red
8.0
5.7
2.2
4.7
7.5
7.2
3.9
4.5
Pine, sugar
4.4
3.9
2.1
.1
5.4
4.4
3.7
1.9
Tine, western white
5.3
5.1
2.2
4.8
6.5
5.2
2.5
1.5
Redeedar, western
4.3
3.4
1.6
1.3
5.1
5.1
1.6
' 2.3
Spruce, red and Sitka
4.7
3.9
1.7
2.0
5.3
4.3
2.6
2.4
5.8
4.8
1.9
2.1
6.5
5.7
3.7
3.3
Whitecedar, northern
5.4
3.6
1.8
1.5
5.9
2.3
2.8
3.0
Whitecedar, Port Orford
5.7
5.2
1.6
1.7
6.2
6.7
2.2
2.8
1 Corrections to the strength properties should be made successively for each one percent change in moisture content
until the total change has been covered.
2 Negative values indicate a decrease in work to maximum load for a decrease in moisture content.
3 For tension values see section 2.5411.
explore the effect of rate of loading on the more important properties; to clarify the
relations among rate of load application, duration of load, and strength; and to correlate
these data with the loadtime relations that may obtain in static testing and in air
plane flight.
When tests of physical properties are made on additional species or on specially
selected wood the results may be made comparable to those in table 23 by adjusting
18
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
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ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS
21
them to 15 percent moisture content (in accordance with table 22) together with the
appropriate use of the factors described in the footnotes to table 23.
For notes on acceptable procedures for static tests and the correction of test results,
see sections 2.12 and 3.01.
2.100. Supplemental notes.
2.1000. Compression perpendicular to grain. Wood does not exhibit a definite
ultimate strength in compression perpendicidar to the grain, particularly when the load
is applied over only a part of the surface, as it is by fittings. Beyond the proportional
limit the load continues to increase slowly until the deformation and crushing become
so severe as to damage seriously the wood in other properties. A factor of 1.33 was
applied to average values of stress at proportional limit to get design values comparable
to those for bending, compression parallel to grain, and shear as shown in table 23.
2.1001. Compression parallel to grain. Available data indicate that the propor
tional limit for hardwoods is about 75 percent and for softwoods about 80 percent of
the maximum crushing strength. Accordingly, design values for fiber stress at propor
tional limit were obtained by multiplying maximum crushingstrength values by a
factor of 0.75 for hardwoods and 0.80 for softwoods.
2.11. Notes on the Use of Values in Table 23.
*2.110. Relation of design values in table 23 to slope of grain. The values given
in table 23 apply for grain slopes as steep as the following:
(a) For compression parallel to grain — 1 in 12.
(£>) For bending and for tension parallel to grain — 1 in 15. When material is used
in which the steepest grain slope is steeper than the above limits, the design values of
table 23 must be reduced according to the percentages in table 24.
Table 24. — Reduction in wood strength for various grain slopes.
Corresponding design value, percent of value in table 23
Static bonding
Compression
Tension
Maximum slope of grain in the member
parallel to
parallel to
grain
grain
Fiber stress
Modulus
Modulus of
Maximum
Modulus of
at proportional
of
elasticity
crushing
rupture
limit
rupture
strength
1 in 15
100
100
88
100
100
1 in 12
98
97
100
85
1 in 10
87
78
91
98
75
1 in 8
78
07
84
94
60
2.111. Tension parallel to grain. Relatively few data are available on the tensile
strength of various species parallel to grain. In the absence of sufficient tensiletest
data upon which to base tension design values, the values used in design for modulus
of rupture are used also for tension. While it is recognized that this is somewhat con
servative, the pronounced effect of stress concentration, slope of grain (table 24) and
other factors upon tensile strength makes the use of conservative values desirable.
Pending further investigation of the effects of stress concentration at bolt holes,
it is recommended that the stress in the area remaining to resist tension at the critical
section through a bolt hole not exceed twothirds the modulus of rupture in static
22
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
bending when crossbanded reinforcing plates are used; otherwise onehalf the modulus
of rupture shall not be exceeded.
2.112. Tension perpendicular to grain. Values of strength of various species in
tension perpendicular to grain have been included for use as a guide in estimating the
adequacy of glued joints subjected to such stresses. For example, the joints between
the upper wing skin and wing framework are subjected to tensile stresses perpendicular
to the grain by reason of the lift forces exerted on the upper skin surface.
Caution must be exercised in the use of these values, since little experience is
available to serve as a guide in relating these design values to the average property.
Considering the variability of this property, however, the possible discontinuity or lack
of uniformity of glue joints, and the probable concentration of stress along the of edges
such joints, the average test values for each species have been multiplied by a factor of
0.5 to obtain the values given in table 23.
2.12. Standard Test Procedures.
2.120. Static bending. In the staticbending test, the resistance of a beam to slow
ly applied loads is measured. The beam is 2 by 2 inches in cross section and 30 inches
long and is supported on roller bearings which rest on knife edges 28 inches apart. Load
is applied at the center of the length through a hard maple block inches wide, having
a compound curvature. The curvature has a radius of 3 inches over the central 2}/g
inches of arc, and is joined by an arc of 2inch radius on each side. The standard place
ment is wjth the annual rings of the specimen horizontal and the loading block bearing
on the side of the piece nearest the pith. A constant rate of deflection (0.1 inch per
minute) is maintained until the specimen fails. Load and deflection are read simul
taneously at suitable intervals.
Figure 23 (a) shows a diagrammatic sketch of the staticbending test setup, and
typical loaddeflection curves for Sitka spruce and yellow birch.
Data on a number of properties are obtained from this test. These are discussed
as follows:
2.1200. Modulus of elasticity (El). The modulus of elasticity is determined from
the slope of the straight line portion of the graph, the steeper the line, the higher being
the modulus. Modulus of elasticity is computed by
P 7.3 p TZ
483 J 4S P 6# K '
The standard static bending test is made under such conditions that shear deformations
are responsible for approximately 10 percent of the deflection. Values of E L from tests
made under such conditions and calculated by the formula shown do not, therefore,
represent the true modulus of elasticity of the material, but an "apparent" modulus of
elasticity.
The use of these values of apparent modulus of elasticity in the usual formulas will
give the deflection of simple beams of ordinary length with but little error. For I and
box beams, where more exact computations are desired, and formulas are used that take
into account the effect of shear deformations, a "true" value of the modulus of elasticity
is necessary and may be had by adding 10 percent to the values in table 23.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
MODULUS LINE
^MAXIMUM
LOAD
SITKA
SPRUCE
MODULUS . ^
YELLOW
LINE^i \
/ MAXIMUM^
BIRCH
f LOAD
/"PROPORTIONAL
/ LIMIT
TEST METHOD
DEFLECT/ON (INCHES)
(a) STA TIC BENDING
^MAXIMUM LOAD
SITKA
SPRUCE
/ PROPORTIONAL
I LIMIT
^MAXIMUM LOAD
YELLOW
BIRCH
/ PROPORTIONAL ~~~~
I LIMIT
TEST METHOD DEFORMATION (INCHES)
(b) COMPRESSION PARALLEL TO GRAIN
NO MAXIMUM
LOAD OBTAINED
\ PROPORTIONAL
SITKA
\ LIMIT
SPRUCE
NO MAXIMUM
C
LOAD OBTAINED
/ ^PROPORTIONAL
I LIMIT
YELLOW
BIRCH
TEST METHOD
DEFORMATION (INCHES)
CO COMPRESSION PERPENDICULAR TO GRAIN
Figure 23. — Standard test methods and typical loaddeflection curves.
24
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
2.1201. Fiber stress at proportional limit (F bp ). The plotted points from which
the early portions of the curves of figure 23 (a) were drawn lie approximately on a
straight line, showing that the deflection is proportional to the load. As the test progresses
however, this proportionality between load and deflection ceases to exist. The point
at which this occurs is known as the proportional limit. The corresponding stress in the
extreme fibers of the beam is known as "fiber stress at proportional limit." Fiber stress
at proportional limit is computed by
P P Lc 1.5 P P L
Fb * 4 I~ bd> (2  2)
2.1202. Modulus of rupture (F h „). Modulus of rupture is computed by the same
formula as was used in computing fiber stress at proportional limit, except that maxi
mum load is used in place of load at proportional limit. Since the formula used is based
upon an assumption of linear variation of stress across the cross section of the beam,
modulus of rupture is not truly a stress existing at time of rupture, but is useful in find
ing the loadcarrying capacity of a beam.
2.1203. Work to maximum load. The energy absorbed by the specimen up to the
maximum load is represented by the area under the loaddeflection curve from the
origin to a vertical line through the abscissa representing the maximum deflection at
which the maximum load is sustained. It is expressed, in table 23, in inchpounds per
cubic inch of specimen. Work to maximum load is computed by
„ 7 , , D area under curve to P max . ,~
Work to P max . = ^^ (2:3)
2.121. Compression parallel to grain. In the compressionparalleltograin test,
a 2 by 2 by 8inch block is compressed in the direction of its length at a constant rate
(0.024 inch per minute). The load is applied through a spherical bearing block, pref
erably of the suspended selfaligning type, to insure uniform distribution of stress. On
some of the specimens, the load and the deformation in a 6inch central gage length are
read simultaneously until the proportional limit is passed. The test is discontinued
when the maximum load is passed and the failure appears.
Figure 23 (b) shows a diagrammatic sketch of the test setup, and typical load
deflection curves for Sitka spruce and yellow birch. Data on a number of properties
are obtained from this test. These are discussed as follows:
2.1210. Modulus of elasticity (£/,, ). The modulus of elasticity is determined from
the slope of the straightline portion of the graph, the steeper the line the higher the
modulus. The modulus of elasticity is computed by
K  i',;. < 2:4)
The value of the modulus of elasticity so determined corresponds to the "true"
value of modulus of elasticity discussed under static bending. Values of the modulus of
elasticity from compressionparalleltograin tests are not published but may be approxi
mated by adding 10 percent to the apparent values shown under static bending in table
23.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
25
2.1211. Fiber stress at proportional limit (F CP ) The plotted points from which
early portions of the curves of figure 23 (b) were drawn lie approximately on a straight
line, showing that the deformation within the gage length is proportional to the load
The point at which this proportionality ceases to exist is known as the proportional
limit and the stress corresponding to the load at proportional limit is the fiber stress at
proportional limit. It is calculated by
Fc P = f (2:5)
2.1212. Maximum crushing strength (F IU ). The maximum crushing strength is
computed by the same formula as used in computing fiber stress at proportional limit ex
cept that maximum load is used in place of load at proportional limit.
2.122. Compression perpendicular to grain. The specimen for the compression
perpendiculartograin test is 2 by 2 inches in cross section and 6 inches long. Pressure
is applied through a steel plate 2 inches wide placed across the center of the specimen
and at right angles to its length. Hence, the plate covers onethird of the surface. The
standard placement of the specimen is with the growth rings vertical. The standard
rate of descent of the movable head is 0.024 inch per minute. Simultaneous readings
of load and compression are taken until the test is discontinued at 0.1inch compression.
Figure 23 (c) shows a diagrammatic sketch of the test setup, and typical load
deflection curves for Sitka spruce and yellow birch.
The principal property determined is the stress at proportional limit (F cp t) which
is calculated by
p _ Load at proportional limit ^.g
cp Width of plate X width of specimen
Tests indicate that the stress at proportional limit when the growth rings are placed
horizontal does not differ greatly from that when the growth rings are vertical. For
design purposes, therefore, the values of strength in compression perpendicular to grain
as given in table 23 may be used regardless of ring placement.
2.123. Shear parallel to grain (F SII ). The shearparalleltograin test is made by
applying force to a 2by 2inch lip projecting % inch from a block 2^2 inches long. The
block is placed in a special tool having a plate that is seated on the lip and moved down
ward at a rate of 0.015 inch per minute. The specimen is supported at the base so that
a J^inch offset exists between the outer edge of the support and the inner edge of the
loading plate.
The shear tool has an adjustable seat in the plate to insure uniform lateral distri
bution of the load. Specimens are so cut that a radial surface of failure is obtained in
some and a tangential surface of failure in others.
The property obtained from the test is the maximum shearing strength parallel
to grain. It is computed by
(2:7)
The value of F su as found when the surface of failure is in a tangential plane does
not differ greatly from that found when the surface of failure is in a radial plane, and
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS
27
the two values have been combined to give the values shown in column 14 of table 23.
2.124. Hardness. Hardness is measured by the load required to embed a 0.444
inch ball to onehalf its diameter in the wood. (The diameter of the ball is such that its
projected area is one square centimeter.) The rate of penetration of the ball is 0.25 inch
per minute. Two penetrations are made on each end, two on a radial, and two on a
tangential surface of the specimen. A special tool makes it easy to determine when the
proper penetration of the ball has been reached. The accompanying load is recorded
as the hardness value.
Values of radial and tangential hardness as determined by the standard test have
been averaged to give the values of side hardness in table 23.
2.125. Tension perpendicular to grain (F, u r). The tensionperpendiculartograin
test is made to determine the resistance of wood across the grain to slowly applied
tensile loads. The test specimen is 2 by 2 inches in cross section, and 2^ inches in overall
length, with a length at midheight of 1 inch. The load is applied with special grips, the
rate of movement of the movable head of the testing machine being 0.25 inch per
minute. Some specimens are cut to give a radial and others to give a tangential surface
of failure.
The only property obtained from this test is the maximum tensile strength perpen
dicular to grain. It is calculated from the formula
F tuT = ^Y 1 < 2:8)
Tests indicate that the plane of failure being tangential or radial makes little
difference in the strength in tension perpendicular to grain. Results from both types
of specimens have, therefore, been combined to give the values shown in table 23.
2.13. Elastic Properties Not Included in Table 23. Certain elastic properties use
ful in design are not included in table 23. The data in table 23 are, in general, based
on large numbers of tests, while the data on the additional elastic properties are based on
relatively few tests. Available data on these properties are included in table 25.
2.130. Moduli of elasticity perpendicular to grain (Et, £/?). The modulus of elas
ticity of wood perpendicular to the grain is designated as Et when the direction is tangen
tial to the annual growth rings, and Er when the direction is radial to the annual growth
rings. Tests have been made to evaluate these elastic properties for only a very few
species (table 25), and, until further information is available, it is recommended that
the ratios of Et/El and Er/El be taken as 0.045 and 0.085, respectively, for all species
not listed in the tables. Values of El are given in table 23.
*2.131. Moduli of rigidity (Glt, Glr, Grt) The modulus of elasticity in shear,
or the modulus of rigidity as it is called, must be associated with shear deformation in
one of the three mutually perpendicular planes defined by the L, T, and R directions,
and with shear stresses in the other two. The symbol for modulus of rigidity has sub
scripts denoting the plane of deformation. Thus the modulus of rigidity Glt refers to
shear deformations in the LT plane resulting from shear stresses in the LR and RT
planes. Values of these moduli for a few species are given in table 25. For other species
not listed, it is recommended that the ratios Glt/El =0.05, Glr/El, = 0.06, and
Grt/El = 0.01 be used in evaluating the various moduli of rigidity.
28
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
*2.132. Poisson's ratios (\x). The Poisson's ratio relating to the contraction in
the T direction under a tensile stress acting in the L direction, and thus normal to the
RT plane, is designated as [Ilt', Vlr, Vrt, ^rl, [ltr, and \xtl have similar significance,
the first letter of the subscript in each relating to the direction of stress and the second
to the direction of the lateral deformation. The two letters of the subscript may be
interchanged without changing the meaning when G is considered but the same is not
true for \x. Information on Poisson's ratios for wood is meager and values for only a
few species are given in table 25.
2.14. Stressstrain relations. (See section 2.56.)
2.2. COLUMNS.
2.20. Primary Failure. The allowable stresses for solid wood columns are given
by the following formulas:
Long columns
10 ^ .
9
(t)
(2:9)
L\ V 15E L
Feu
() =
V p /cr
Short columns (ref. 220)
where: K = (—)
\ a /cr
These formulas are reproduced graphically in figure 24 for solid wood struts of a
number of species.
2.21. Local Buckling and Twisting Failure. The formulas given in section 2.20
do not apply when columns with thin outstanding flanges or low torsional rigidity are
subject to local buckling or twisting failure. For such cases, the allowable stresses are
given by the following formulas :
Local buckling (torsionally rigid columns)
F c = 0.07 E L (^) 2 psi (when p6) (2:11)
Twisting failure (torsionally weak columns)
F = 0.044 E L (A' psi (when ^>5) (2:12)
When the widththickness ratio (b/t) of the outstanding flange is less than the
values noted, the column formulas of section 2.20 should be used. Failure due to local
buckling or twisting can occur only when the critical stress for these types of failure is
less than the stress required to cause primary failure. For unconventional shapes, tests
should be conducted to determine suitable column curves (ref. 232).
STRENGTH OP WOOD AND PLYWOOD ELEMENTS
29
o
isd Ml S S3 HIS NWniOD 319VM011V 7 J
30
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
2.22. Lateral Buckling. When subjected to axial compressive loads, beams will
act as columns tending to fail through lateral buckling. The usual column formulas
(2:9 and 2:10) will apply except that when two beams are interconnected by ribs so that
they will deflect together (laterally), the total end load carried by both beams will be
the sum of the critical end loads for the individual beams.
The column lengths will usually be the length of a drag bay in a conventional wing.
A restraint coefficient of 1.0 will be applicable unless the construction is such that addi
tional restraint is afforded by the leading edge or similar parts. Certain rules for such
conditions will be found in the requirements of the certificating or procuring agencies.
2.3. BEAMS.
2.30. Form Factors. When other than solid rectangular cross sections are used for
beams, (Ibeams or box beams), the staticbending strength properties given in table
23 must be multiplied by a "form factor" for design purposes. This form factor is the
ratio of either the fiber stress at proportional limit or the modulus of rupture (in bending)
of the particular section to the same property of a standard 2inch square specimen
of that material. The proportional limit form factor (FF P ) is given by the formula:
FF P = 0.58+0.42 (k (2:13)
and the modulus of rupture form factor (FF U ) by the formula:
FF U = 0.50+0.50 (K (2:14)
where
b' = tota web thickness
b = total flange width (including any web(s))
K = constant obtained from figure 25.
Formulas 2:13 and 2:14 cannot be used to determine the form factors of sections
in which the top and bottom edges of the beam are not perpendicular to the vertical
axis of the beam. In such cases, it is first necessary to convert the section to an equivalent
section whose height equals the mean height of the original section, and whose width
and flange areas equal those of the original section, as shown in figure 25. The fact
that the two beams of each pair shown in figure 25 developed practically the same
maximum load in test demonstrates the validity of this conversion (ref. 216 and 221).
Tests have indicated that the modulus of rupture which can be developed by a
beam of rectangular cross section decreases with the height. Sufficient data are not
available to permit exact evaluation of the reduction as the height increases, but where
deep beams of rectangular cross section are to be used, thought should be given to the
reduction of the value for modulus of rupture given in table 23.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
31
35
5
15
ioo
£=7.5£ ± = &33
c d
L4.73 ± = 5.33
o Maximum load = 3200 lb. '■*» f*"~^~i , f —
£ = 4.73
FFu= .86 FF V = .74
FF V ±= 357 FF V ± = 3.50 FF V ± = 6.7/ FF V ±,6.76
± = 9.88
FF V = .68
±= 10.40
FF U = .65
Figure 25. — Formfactor curve and equivalent beam sections.
32
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
2.31. Torsional Instability. It Is possible for deep thin beams to fail through
torsional instability at loads less than those indicated by the usual beam formula. Ref
erence 222 gives formulas for calculating the strength of such beams for various condi
tions of end restraint. However, in view of the difficulty of accurately evaluating the
modulus of rigidity and endfixity, it is always advisable to conduct static tests of a
typical specimen. This will apply to cases in which the ratio of the moment of inertia
about the horizontal axis to the moment of inertia about the vertical axis exceeds approxi
mately 25 (ref. 221 and 222).
2.32. Combined Loadings.
2.320. General. Because of the variation of the strength properties of wood with
the direction of loading with respect to the grain, no general rules for combined loadings
can be presented, other than those for combined bending and compression given in
section 2.321, and those for combined bending and tension given in section 2.322. When
unusual loading combinations exist, static tests should be conducted to determine the
desired information.
2.321. Bending and compression. When subjected to combined bending and
compression, the allowable stress for spruce, western hemlock, noble fir, and yellow
poplar beams can be determined from figure 26; that for Douglasfir beams can be
determined from figure 27. The charts are based on a method of analysis developed by
the Forest Products Laboratory (ref. 222 and 229).
The curves of figures 26 and 27 are based on the use of a secondpower parabola
for columns of intermediate length. The use of these curves has given acceptable results,
but later data on columns under compressive loading only has demonstrated that the use
of a fourthpower parabola for columns of intermediate length, as in figure 24, is per
missible. New combinedloading curves, based on the use of a fourthpower parabola
will be presented in connection with other contemplated revisions. On these figures,
the horizontal family of curves indicates the proportional limit under combined bending
and compression, and the vertical family the effect of various slenderness ratios on bend
ing. The allowable stress, F bc , under combined load is found as follows :
(1) For the cross section of the given beam, find the proportional limit in bending
and the modulus of rupture from the ratios of compressionflange thickness to total
depth and of web thickness to total width, locating points such as A and B. 
(2) Project points A and B to the central line, obtaining such points as C and D.
(3) Locate a point such as E, indicating the proportional limit of the given section
under combined bending and compression. This point will be at the intersection of the
curve of the "horizontal" family through C and the curve of the slenderness ratio cor
responding to the distance between points of inflection.
(4) Draw ED.
(5) Locate F on ED, with an abscissa equal to the computed ratio of bending to
total stress. The ordinate of F represents the desired value of the allowable stress.
The following rules should be observed in the use of figures 26 and 27:
(1) The length to be used in computing the slenderness ratio, L/p should be de
termined as follows :
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
33
«o ^ "J
34
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(a) If there are no points of inflection between supports, L should be taken as the
distance between supports.
(6) If there are two points of inflection between supports, L should be taken as the
distance between these points of inflection when calculating the allowable strength of
any section included therein.
(c) When calculating the allowable strength of a section between a point of in
flection and an intermediate support of a continuous beam, L should be taken as the
distance between the points of inflection adjacent to the support on either side.
(d) When investigating a section adjacent to an end support, L should be taken
as twice the distance between the support and the adjacent point of inflection, except
that it need not exceed the distance between supports.
(2) In computing the value of p for use in determining the slenderness ratio,
L/p, filler blocks should be neglected and, in the case of tapered spars, the average value
should be used.
(3) In computing the modulus of rupture and the proportional limit in bending,
the properties of the section being investigated should be used. Filler blocks may be
included in the section for this purpose. When computing the form factor of box spars,
the total thicknesses of both webs should be used.
2.322. Bending and tension. When tensile axial loads exist, the maximum com
puted stress on the tension flange should not exceed the modulus of rupture of a solid
beam in pure bending. Unless the tensile load is relatively large, the compression flange
should also be checked, using the modulus of rupture corrected for form factor.
2.33. Shear Webs. See section 2.72.
2.34. Beam Section Efficiency. In order to obtain the maximum bending efficiency
of either I or box beams, the unequal flange dimensions can be determined by first
designing a symmetrical beam of equal flanges. The amount of material to be trans
ferred from the tension side to the compression side, keeping the total crosssectional
area, height and width constant, is given by the following equation (ref. 221) :
x
Abh 2 VA 2 b 2 h 4 4:AI s bhwD
2wDbh
(2:15)
where :
A = total area of the cross section
b = total width
h = total depth
w = width of flange
D = clear distance between flanges
I s = moment of inertia of the symmetrical section
x = thickness to be taken from tension flange and
added to compression flange.
In using this equation, the following procedure is to be followed :
(a) Determine the section modulus required.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
35
Nl OS" if 3d ff7 JO SaNVMOHl Nl **J fttiflS 319VM0nV
36
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(b) Determine the sizes of flanges of equal size to give the required section modulus.
(c) Using equation (2:15), compute the thickness of material to be transferred
from the tension flange to the compression flange. The procedure thus far will result
in a section modulus greater than required. To obtain a beam of the required section
modulus, either (d) or (e) may be followed.
(d) Calculate the ratio of depth of tension flange to compression flange and design
a section having flanges with this ratio and the required section modulus, or
(e) Carry out steps (a), (6), and (c) starting with a symmetrical section having a
section modulus less than that required until an unsymmetrical section having the re
quired section modulus is obtained.
(/) Beams designed according to the foregoing procedure should always be checked
for adequacy of glue area between webs and tension flange. This consideration may
govern the thickness of the tension flange.
2.4. TORSION.
2.40. General. The torsional deformation of wood is related to the three moduli
of rigidity, Glt, Glr, and Grt When a member is twisted about an axis parallel to the
grain, Grt is not involved; when twisted about an axis radial to the grain direction,
Glt is not involved; when twisted about an axis tangential to the grain direction, Glr
is not involved. No general relationship has been found for the relative magnitudes of
G L r, Glt, and G RT . (Table 25).
2.41. Torsional Properties. The "mean modulus of rigidity" (G) taken as V\?> of
El, may be safely used in the standard formulas for computing the torsional rigidities
and internal shear stresses of solid wood members twisted about an axis parallel to the
grain direction. Torsion formulas for a number of simple sections are given in table 26.
For solidwood members the allowable ultimate torsional shear stress (F st ) may be taken
as the allowable shear stress parallel to the grain (column 14 in table 23) multiplied by
1.18 that is, F s( = 1.18 F su . The allowable torsional shear stress at the proportional
limit may be taken as twothirds of F st . The torsional strength and rigidity of box
beams having plywood webs are given in section 2.74.
T\ble 26. — Formulas for torsion on symmetrical sections
Section
Angle of twist in radians
Maximum shear stress
Circular tube
Circle.
Ellipse
fs =— at ends of short diameter.
■nab 2
TD
G 7ra = & 3
Rectangle 3
Square' 2
fs = —  (approx.)
fs = ^ V5a\9b) a( . jjjjdpoint of long side.
1 2a =major axis: 2b =minor axis,
2 2a =side of square.
3 2a = long side, 2b = short side.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
37
2.5. BASIC STRENGTH AND ELASTIC PROPERTIES OF PLYWOOD.
2.50. General. Plywood is usually made with an odd number of sheets or plies of
veneer with the grain direction of adjacent plies at right angles. Depending upon the
method by which the veneer is cut, it is known as rotarycut, sliced, or sawed veneer.
Generally, the construction is symmetrical ; that is, plies of the same species, thickness,
and grain direction are placed in pairs at equal distances from the central ply. Lack of
symmetry results in twisting and warping of the finished panel. The disparity between
the properties of wood in directions parallel to and across the grain is reduced by reason
of the arrangement of the material in plywood. By placing some of the material with
its strong direction (parallel to grain) at right angles to the remainder, the strengths in
the two directions become more or less equalized. Since shrinkage of wood in the longi
tudinal direction is practically negligible, the transverse shrinkage of each ply is re
strained by the adjacent plies. Thus, the shrinking and swelling of plywood for a given
change in moisture content is less than for solid wood.
fa) Ptywooo fe) sr/?A/A/ (cjr stress
Figure 28. — Threeply plywood beam in bending.
Table 27. — Veneer species for aircraft plywood
Group I (high density) 1 ' 2
Group II (medium density) 2
Group III (low density) 5
American beech
Birch (Alaska and paper)
Basswood
Birch (sweet and yellow)
Khaya species (socalled "African mahogany")
Yellowpoplar
Maple (.hard)
Southern magnolia
Port Orford whitecedar
Pecan
Mahogany (from tropical America)
Spruce (red, Sitka, and white)
Maple (soft)
(quartersliced)
Sweetgum
Ponderosa pine (quartersliced)
Water tupelo
Sugar pine
Black walnut
Noble fir (quartersliced)
Douglasfir (quartersliced)
Western hemlock (quartersliced)
American elm (quartersliced)
Redwood (quartersliced)
Sycamore
1 Where hardness, resistance to abrasion, and high strength of fastening are desired, Group I woods should be used
for face stock.
2 Where finish is desired, or where the plywood is to be steamed and bent into a form in which it is to remain, species
of Group I and II should be used.
3 Group III species are used principally for core stock and crossbanding. However, where high bending strength or
freedom from buckling at minimum weight is desired, plywood made entirely from species of Group III is recommended.
38
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
The tendency of plywood to split is considerably less than for solid wood as a
result of the crossbanded construction. While many woods are cut into veneer, those
species which have been approved for use in aircraft plywood are listed in table 27.
2.51. Analysis of Plywood Strength Properties. The analysis of the strength and
elastic properties of plywood is complicated by the fact that the elastic moduli of ad
jacent layers are different. This is illustrated in figure 28 for bending of a threeply
panel. Assuming that strain is proportional to distance from the neutral axis, stresses
on contiguous sides of a glue joint will be different by reason of the difference in the
modulus of elasticity in adjacent layers. This results in a distribution of stress across
the cross section as shown in figure 28 (c). Similar irregular stress distribution will be
obtained for plywood subjected to other types of loading.
From this it may be seen that the strength and elastic properties of plywood are
dependent not only upon the strength of the material and the dimensions of the mem
f/:2:/j j^zr^/.y.vj
s/=>i y^/;2. 2:2:/) spl y (/:/:/:/:/)
Figure 29. — Typical plywood constructions. Arrows indicate grain direction of each ply.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
39
ber, as for a solid piece, but also upon the number of plies, their relative thickness, and
the species used in the individual plies. In addition, plywood may be used with the
direction of the face plies at angles other than 0° or 90° to the direction of principal
stress and, in special cases, the grain direction of adjacent plies may be oriented at angles
other than 90°.
In general, plywood for aircraft use has the grain direction (the longitudinal direc
tion) of adjacent plies at right angles. The strength and elastic properties of the plywood
are dependent upon the properties of solid wood along and across the grain as illustrated
in figure 29.
Considerable information (table 23) on the properties of wood parallel to the grain
is available, but the data on properties acrossthegrain are less complete. Sufficient
data are available, however, so that the elastic properties of wood in the two directions
can be related with reasonable accuracy to the plywood properties. On this basis formulas
are given which will enable the designer, knowing the number, relative thickness and
species of plies, to compute the properties of plywood from the data given in table 23.
The formulas given are only for plywood having the grain direction of adjacent plies
at right angles and are applicable only to certain directions of stress. The limitations
on the angle between the face grain and the direction of principal stress have been noted
in each section. The formulas are intended for use only in these cases, and the inter
polation must not be used to obtain values for intermediate angles unless specific in
formation on these angles is given. Computed values of certain of the strength and
elastic properties for many of the commonly used species and constructions of plywood
are given in section 2.540.
2.52. Basic Formulas. For purposes of discussion, plywood structural shapes may
be conveniently separated into two groups : (a) elements acting as prisms, columns, and
beams, and (b) panels. The fundamental difference between these two groups is that, in
group (a) the plywood is supported or restrained only on two opposite edges, while in
group (b) the plywood is supported or restrained on more than two edges. It is essential
that this fundamental difference between the two groups be kept in mind during the
application of the formulas 2 given here and in later sections.
(1) The effective moduli of elasticity of plywood in tension or compression are :
E a — measured parallel to side a for panels (sec. 2.710)
Eb — measured perpendicular to side a for panels (sec. 2.710)
E w — measured parallel to (with) the face grain
E x — measured perpendicular to (across) the face grain
and are determined as
! When computing the various moduli of elasticity ior plywood of balanced construction and all plies of the same
species, the following relationship will be found helpful:
E L +E T = E a +E b =E 1 +E s =E w +Es=E fw +E fI
If the veneers are quartersliced rather than rotarycut, the term Ex should be replaced by Er.
tl
(2:16)
■
40 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
where :
A = total cross section area.
Ai = axea, of i' h ply.
E; = modulus of elasticity of ply measured in the same direction as the perti
nent desired E (as E a , Eb, E w , or E x ). The value of Ei is equal to 1.1 El
(table 23), or Et, or Er, (table 25) as applicable.
(2) The effective moduli of elasticity of plywood in bending are :
Ei — measured parallel to side a for panels.
Ei — measured perpendicular to side a for panels.
E fw — measured parallel to (with) the face grain,
/^—measured perpendicular to (across) the face grain and
are determined as
i =n
= y\ Ei h (2:17)
/_
i = l
Where :
Er — as defined under (1).
7= moment of inertia of the total cross section about the centerline, measured
in the same direction as the pertinent desired E (namely, E x , E2, E fw , or E fx ).
7,= moment of inertia of the i' h ply about the neutral axis of the same total cross
section. For symmetrically constructed plywood, the neutral axis to be used
in determining I{ will be the centerline of the cross section. For unsymmetrical
plywood constructions, the neutral axis is usually not the centerline of the
geometrical section. In this case the distance from this neutral axis to the
extreme compression fiber is given by the equation:
AiEid
(2:18)
AiEi
i = l~
%
= n
\
/
i
= 1
i
= n
\
/
where :
c, = distance from the extreme compression fiber to the center of the i th ply.
(3) In calculating the bending strength (not stiffness) of plywood strips in bending
having the face grain direction perpendicular to the span, a modulus E' fx , similar to
E fx is to be used. For plywood made of five or more plies, the use of E fx for E' fx in
strength calculations will result in but relatively small error. The value of E' fx may be
calculated in the same manner as that used in calculating E fx except that the effect of
the outer ply on the tension side is neglected. The location of the neutral axes used in
calculating E fx and E' fx will be different. The value of E' fx may also be calculated from
the following formula:
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
41
E'^E fx +^ (c'^+^^r (C^) 2 (2.19;
where:
" tE x
1 l, Ei
c =
tE r 1
tf Et
= distance from neutral axis to extreme fiber of the outermost longitudinal ply.
Et pertains to the species of the face ply.
*(4) The modulus of rigidity (modulus of elasticity in shear) of solid wood involves
the sheer moduli Glt, Glr, and Gut
As mentioned in section 2.131, little information is available on this elastic property,
and a "mean" modulus of ridigity is ordinarily used for wood. Similarly for plywood,
a value of modulus of rigidity based on the "mean" modulus of rigidity for solid wood
may be used.
For plywood (all plies the same species) having the face grain parallel or perpendicu
lar to the direction of principal shearing stress, the modulus of rigidity may be taken
the same as for solid wood. For plywood having the face grain at 45° to the direction
of principal shearing stress, the modulus of rigidity may be taken as five times the "mean"
modulus of rigidity for solid wood (sec. 2.41). Thus, the modulus of rigidity for 45° ply
wood is approximately % of the bending modulus of elasticity parallel to the grain of
solid wood (sec. 2.56) as given in table 23.
The theoretical treatment of the elastic properties of plywood involves the moduli
of rigidity G wx and G fwx . The apparent modulus of rigidity in the plane of the plywood is
i = n
G wx =\ CnU (2:20)
/
i = l
where the summation is taken over all plies in a section perpendicular to either the a or b
directions using the modulus of rigidity in each ply in the wx plane.
When the plywood is made of a single species of wood,
G wx = Glt for rotarycut veneer.
G wx = Glr for quartersliced veneer
The apparent modulus of rigidity of plywood for use in formulas involving the
bending of plywood plates into double curvature is
i = n
G /wx =— y QL+t^Gi (2:21)
/
i=l
where yi = distance from the neutral axis to the center of the i th ply.
*(5) Poisson's ration ((x). Although there is very little information available on
the values of Poisson's ratios for plywood, a brief summary of their significance is given.
42
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
The effective Poisson's ratio of plywood in tension or compression (no flexure) is the
ratio of the contraction along the x direction to extension along the w direction due to
tensile stress acting in the w direction and thus normal to the xt plane, or
i = n
^•* = 7"p~/ U{E x )i ([k wx )i (2:22)
tE * i = l
modulus of elasticity of the i' h ply in the x direction.
Poisson's ratio of contraction along the x direction to extension in the w
direction due to a tensile stress acting in the w direction and thus normal
to the xt plane of the i th ply.
i =n
i = l
If all plies are of the same species of rotarycut veneer
\x wx = El vtl/E x
\j. X w=El \>tl/E w
If all plies are of the same species of quartersliced veneer
\>. wx = El vrl/E x
^ tu =El vrl/E w
These formulas give close approximations of the apparent Poisson's ratios in these
two directions when the stress is simple tension or compression. For more accurate
formulas than 2 :22 and 2 :23 see reference 225. For Poisson's ratio at an angle to the
grain see section 2.56.
*2.5 3. Approximate Methods for Calculating Plywood Strengths. Table 28 gives
some approximate methods of calculating the various strength properties of plywood.
These simplified methods will be found very useful in obtaining estimates on the strength
of plywood, but cannot be relied upon to give results which are comparable to those
obtained with the more accurate methods.
2.54. MoistureStrength Relations for Plywood.
2.540. General. The design values given in the plywood strengthproperty tables
29 and 210 were calculated from the strength properties of solid wood as given in
table 23.
Adjustment factors by which strength properties of solid wood may be corrected
for moisture content are shown in table 22. For plywood, moisture corrections are
dependent on many variable factors, such as grain direction, combinations of species,
and relative thicknesses of plies in each direction, so that any rational method of cor
rection is quite laborious. An approximate method for making moisture corrections to
plywood is given in the succeeding sections.
2.541. Approximate methods for making moisture corrections for plywood
strength properties. A limited number of compression, bending, and shear tests of
spruce and Douglasfir plywood of a few constructions at moisture content values
where :
(E x )i =
(*wz)« =
Similarly
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
43
ranging approximately from 6 to 15 percent has indicated that use of the following
simplified methods of correcting plywood strength properties will be satisfactory.
2.5410. Moisture corrections for plywood compressive strength (0° or 90° to
face grain direction). Moisture adjustments to the compressive strength of plywood,
either parallel or perpendicular to the face grain direction, may be made by direct use of
the correction constants given in column (6) of table 22.
When more than one species is used in the plywood, the correction constant should
be taken for that species having its grain direction parallel to the applied load.
When plies of two species have their grain direction parallel to the applied load, the
plywood correction constant should be determined by taking the mean value of the cor
rection constants for the two species based on the relative areas of the longitudinal plies
of each.
*2.54ll. Moisture correction for plywood tensile strength (0° or 90° to face
grain direction). Data on the effect of moisture on the tensile strength of plywood
are lacking. Limited data indicate that the effect on the tensile strength of wood is about
onethird as great as on modulus of rupture. The suggested procedure for adjusting the
tensile strength of plywood is to follow that for compressive strength as given in the
preceding section, using onethird of the correction factors given for modulus of rupture
in column 3 of table 22.
*2.5412. Moisture corrections for plywood shear strength (0° or 90° to face
grain direction). Moisture adjustments to the shear strength of plywood, either
parallel or perpendicular to the face grain direction, F swx , may be made by direct use
of empirical correction constants equal to those given in column (8) of table 22 for
shear. The use of such moisture adjustment to the shear strength of plywood is not
applicable when a moisture content of less than 7 percent is involved.
When more than one species is used, the correction constant should be determined
on the basis of the relative areas of each species, considering all plies.
2.5413. Moisture corrections for plywood compressive strength (any angle to
face grain direction). The compression strength of plywood at any moisture content,
and at any angle to the face grain direction, may be found by use of equation 2:19 after
first correcting the compression terms F cuw and F cux in accordance with section 2.5410.
2.5414. Moisture corrections for plywood tensile strength (any angle to face
grain direction). The tension strength of plywood at any moisture content, and at any
angle to the face grain direction, may be found by use of equation 2:50 after first cor
recting the tension terms F tuw and F tux in accordance with section 2.5411, and the shear
term F swx in accordance with section 2.5412.
2.5415. Moisture corrections for plywood shear strength (any angle to face grain
direction). The shear strength of plywood at any nioisture content, and at any angle
to the face grain direction, may be found by use of equations 2:51 or 2:52 after first
correcting the various terms in these equations by the methods outlined in the foregoing
sections.
2.55. Specific GravityStrength Relations for Plywood. As in solid wood, the
strength and elastic properties of plywood increase with an increase in specific gravity.
The magnitude of this strength increase, however, cannot be determined by the same
convenient exponential equation given in table 21.
44
ANC BULLETIN— DESIGN OF "WOOD AIRCRAFT STRUCTURES
Table 28. — Approximate methods jor calculating the strength and stiffness oj plywood 1
Property
Direction of stress with respect
to direction of face grain
Portion of crosssectional area
to be considered
Allowables expressed as
proportion of strength values
given in table 23
Ultimate tensile.
Ultimate compressive
Shear
Shear in plane of plies
Parallel (Ff UW ) or perpen
dicular (F tUl )
±45°
Parallel (Fcmu) or perpen
dicular (F CT , X )
±45" {Fcuas")
Parallel or perpendicular (F^^)
±45° . .'
Parallel, perpendicular, or + 45"
Load in bending.
Parallel or perpendicular.
Deflection in bending
Parallel or perpendicular
Deformation in ten
sion or compression.
Bearing at right angles
to plane of plywood.
Parallel or perpendicular .
Parallel plies 2 only
Full crosssectional area
Parallel plies 2 only
Full crosssectional area
Full crosssectional area
Full crosssectional area
Joints between ribs, spars, etc.
and continuous stressed ply
wood coverings; joints be
tween webs (plywood) and
flanges of I and boxbeams;
joints between ribs, spars,
etc., and stressed plywood
panels when plywood ter
minates at joint — use shear
area over support.
Bending moment M=KfI/c'
where I = moment of inertia
computed on basis of par
allel plies only; c' =distance
from neutral axis to outer
fiber of outermost ply hav
ing its grain in direction of
span; K = 1.50 for threeply
plywood having grain of
outer plies perpendicular to
span, if =0.85 for all other
plywood.
Deflection may be calculated
by the usual formulas, tak
ing as the moment of inertia
that of the parallel plies
plus 1/20 that of the per
pendicular plies. (Whenface
plies are parallel, the calcu
lation may be simplified,
with but little error, by tak
ing the moment of inertia as
that of the parallel plies
only).
Parallel plies 2 only
Loaded area .
Modulus of rupture.
Onefourth modulus of rupture.
Maximum crushing strength or
fiber stress at proportional
limit, as required.
Onethird maximum crushing
strength or onethird fiber
stress at proportional limit,
as required.
1.18 times the shearing strength
parallel to grain.
2.35 times theshearing strength
parallel to grain.
Onethird the shearing strength
parallel to grain for the
weakest species.
Modulus of rupture or fiber
stress at proportional limit,
as required.
Modulus of elasticity.
Modulus of elasticity.
Compression perpendicular to
grain.
• 1 These simplified strength calculations are to be used only as a rough guide in preliminary design work, and are not
acceptable for final design when the results obtained differ considerably from those obtained by the more accurate methods
given in this bulletin.
2 By "parallel plies" is meant those plies whose grain direction is parallel to the direction of principal stress.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
45
In the manufacture of plywood, no requirements have been set up to control the
specific gravity of the individual veneers and consequently there is no assurance that the
final plywood specific gravity will fall within a certain range. The "weight per square
foot" column in table 29 for various plywood constructions has been based on the
average specific gravity values for wood listed in table 23.
The strength properties for a piece of plywood are merely the composite strengths
of each individual veneer in the direction being considered. Therefore, to make a ra
tional specific gravity correction to plywood strength test data, it is first necessary to
determine the specific gravity of each individual veneer and then correct its strength
properties to correspond to the average specific gravity value given in table 23 for that
species. To do this, of course, is impractical and the problem is further complicated by
the effect of glue impregnation.
When substantiating the strength of a plywood structure, or when establishing de
sign values from static tests, the weight per square foot of the plywood used in the
specimens should be near the values given in table 29 to minimize the effect of high
or low specific gravity values.
2.56. StressStrain Relations for Wood and Plywood. When stresses are applied to
wood or plywood in a direction at an angle to the grain, the resulting strains are quite
different from those obtained in isotropic materials. Mohr's stressandstrain circles are
a means of showing, graphically, the relation of stress or strain in one direction to the stress
Figure 210. — General stress distribution in plywood.
46
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
or strain in any other direction and are an aid in the visualization and evaluation of these
relations. Reference 225 treats extensively the general problem of the use of Mohr's
circles in connection with wood and plywood. However, only a limited general treatment
is presented herein, together with a few specific examples of calculated Mohr'scircle
constants and of the use of the Mohr's circle in determining the elastic properties of
45° plywood.
2.560. Derivation of general stressstrain relations for plywood. In this section
is presented the general method of analysis that is applicable both to simple stress (either
direct tension, compression, or shear acting independently) and also to combinations of
stresses.
2.5600. Obtaining strains from given stresses. Assume a stress distribution in a
piece of plywood as shown upon the outer square in figure 210 (direction of arrows
indicates positive direction). The stress circle can be drawn by use of the following
equations as shown in figure 211, and the stresses parallel and perpendicular to the
facegrain direction can be determined.
/
(2:24)
R = V (/iC) 2 +(/ sl ) 2
(2:25)
D '*ECTI0H
NORMAL
STRESS
+
C
+
Figure 211. — Stress circle for stresses shown in figure 210.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
47
The strains parallel and perpendicular to the facegrain direction can be found by
use of the equations
— p*. e x =J§ w~V.«, e sw =j^ (2:26)
Ihw &x & x &w ^(Ju
where :
[x wx and y. xw are given by equations 2:22 and 2:23, respectively.
The strain circle can then be drawn, by the following equations, as shown in figure
212 and the strains in any direction can be determined.
c=(e w +ex) (2:27)
r = V (e w c) 2 +(e sw y (2:28)
Thus, curves similar to those in figures 216 to 219 can be constructed by assuming a
stress of 1 pound per square inch to be applied at various angles to the facegrain direction
and solving for the values of c and r for each of these angles.
Figure 212. — Strain circle resulting from equation (2:26).
48
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
2.5601. Obtaining stresses from given strains. The foregoing process can be re
versed if strains are given and stresses required. For this purpose strains are usually
measured in the three directions shown in figure 213. The strain circle can be drawn,
by use of the following equations, as shown in figure 214, and the strains parallel and
perpendicular to the face grain can be found.
Figure 213. — Directions of measured strains.
Figure 214. — Strain circle for measured strains.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
49
c = ^(C'+c^) e,,=e 8 —c r = y/(e, — c)W(e»,.2) (2:29)
The stresses parallel and perpendicular to the facegrain direction can be obtained
from the following equations:
fw&w j_ ( — — s fx = I!i x , — — fsw = 2G wz e sw (2:30)
The stress circle can then be drawn, by the use of the following equations, as shown
in figure 215, and the stress at any angle to the face grain direction may be found:
C=~ (U+fx) (2:31)
R = V(UCy+(f aw )* (2:32)
/SHEAR STRESS
\ NORMAL
ISTRL55
v — rr~ +
c
Figure 215. — Stress circle resulting from equations (2:30).
2.561. Stressstrain relations for specific cases.
*2.56lO. Stressandstraincircle constants. Stressandstraincircle constants have
been calculated for unit stress (1 pound per square inch) for plywood made of four differ
ent species and having constructions incorporating various ratios of areas of plies running
in one direction, to total plywood area. These are plotted in figures 216 to 219 and
50
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
have been calculated by use of the elastic constants that were obtained experimentally
by Jenkin (ref. 26) and which are presented in the first four lines of table 25. The
designer may, by the use of the general relations derived in section 2.540 (or in reference
UNIT OF TENSILE STRESS  ROTARY % • 60'/. UNIT OF TENSILE STRESS ROTARY £ • SOX
Figure 216. — Strain circle constants for rotarycut plywood subjected to tension or compression.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
51
225) and elasticconstant data obtained from table 25 or section 2.13, calculate the
stressandstraincircle constants applicable to any particular plywood construction.
Figures 216 and 217 cover simple tension in the plane of plywood made of rotary
Figure 217. — Strain circle constants for sliced plywood subjected to tension or compression.
52
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
I t M WALNUT
'0' 10' 20' JO' 40' SO' 60' 70' SO' 90
$
WIT OF TENSILE AND COMPRESSIVE STRESSES  ROTARY
C 10' iO' 30' 40' SO' 60" 70' SO' 90"
6
UNIT OF TENSILE AND COMPRESSIVE STRESSES  ROTARY £ SO'/.
UNIT OF TENSILE AND COMPRESSIVE STRESSES  ROTARY
Figure 218. — Strain circle constants
V 10' 20' JO' to' SO' 60' 70' so' sor"
UNIT OF TENSILE AND COMPRESSIVE STRESSES ~ ROTARY 30%
1* . 1 ■ — — 1 1 1 ! 6
0' 10' 10' 30 40 SO 60' 70' 60 «T
S
UNIT OF TENSILE AND COMPRESSIVE STRESSES  ROTARY yf'lOZ
10' To' 30' W 60' TO' SO' 30,
I
UNIT OF TENSILE AND COMPRESSIVE STRESSES  ROTARY ^ SOX
rotarycut plywood subjected to shear.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
53
Figure 219. — Strain circle constants for sliced plywood subjected to shear.
54
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
cut and sliced veneers, respectively. Figures 218 and 219 cover tension in one direction
and equal compression in a direction 90° to the tension, for plywood made of rotarycut
and sliced veneer, respectively. The combined action of these two stresses is equivalent
to a shear stress equal to the tensile stress and acting at an angle of 45° to it.
Each curve sheet applies to a group of plywood constructions in which all the plies
are of the same species and the crosssectional area of all the plies running in one direction
is a certain fraction of the total crosssectional area of the panel. This fraction is denoted
by upon the individual curve sheets. The curve sheets contain curves for spruce,
mahogany, ash, and walnut, computed from the elastic constants for these species given
in the first four lines of table 25. When the same curve applies to two different species,
a line is used denoting one species and the curve labeled with the first letter of the other.
The curves apply only to the simple stress noted above but they can be combined
for more complicated stress by the usual method of combining strain circles when an
isotropic material is considered.
The curves are not accurate at angles 0° and 90° to the grain, and for these angles,
the methods given in section 2.6 should be used. In the use of figures 216 to 219: 
6 = angle 3 between direction of face grain and the principal axis of tension measured
positively counterclockwise from the grain direction to the axis.
<j> = angle 3 between direction of face grain and the principal axis of extension measured
positively counterclockwise from the grain direction to the axis.
r = radius of strain circle.
c = distance between the origin and the center of the strain circle.
2.5611. Stressstrain relations in plywood at 45° to face grain direction. In
this section are presented the specific applications of the general stressstrain relations
given in section 2.560 to plywood loaded at 45° to the face grain.
J
f,
Figure 220. — Plywood in tension at 45° to the face grain direction.
s When becomes less than 50 percent, the same figures may be used provided the angles 6 and <J> are taken 90° to
A
the face grain: that is, the plies of predominant thickness should always be considered as the face plies.
STRENGTH OP WOOD AND PLYWOOD ELEMENTS
55
2.56110. Tension at 45° to face grain. This case is shown in figure 220.
Equations (2:24) and (2:25) yield:
C=gfrfoTf t =0 (2.33)
R=f t ioTf tl =0 (2:34)
From this the stress circle can be drawn, as shown in figure 221.
The circle passes through the origin, since C = R, and :
t It t It t It (2.35)
JW~^Jl Jx—qJ1 JSW—^Jt
Acting parallel to the face grain is/„ and/ SJ ., and/ SU) acts at right angles to these two.
The strains in these directions can be obtained from equation (2:26).
Figure 221. — Stress circle for plywood in tension at 45° to the face grain direction.
56
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
From these, the strain circle can be drawn, as shown in figure 222. Figure 222 is
not based upon actual quantitative values applicable to any particular plywood con
struction, but upon the general assumption that E w >E X (e w <e x ). For this general case,
the principal axis of strain is not parallel to the direction of the tensile stress.
SHEAR STRAIN
Figure 222. — Strain circle for plywood in tension at 45° to the face grain direction.
The modulus of elasticity at 45° to the direction of the face grain is defined as the
ratio of a tensile (or compressive) stress in this direction to the strain in this direction
which the stress produces, hence
4
(2:37)
Ea5=—=
Ci
~E7
J_ (Aw
1
Gwx
with an associated shear strain
i=ei Kai (A L)
A \ E x E w )
Values of G wx can be calculated from equation 2:20. Values of y. wx , \x. xw can be calculated
from equations 2:22 and 2:23 and notes thereunder.
Where E X = E W (as in balanced construction of one species):
2E W
E 1.5—'
E u
and e a i —0
(2:38)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
57
i
In a balanced construction the equation E is =^r, where c and r are obtained from
figures 216 through 219, may also be used to obtain E, if> .
2.56111. Shear at 45° to the face grain. This case is shown in figure 223. Equa
tions (2:24) and (2:25) yield:
C=0 as/, and/ 2 = (2:39)
ft=/ sl as C and/,=0 (2:40)
The center of the stress circle is at the origin and can be drawn as shown in figure 224.
This shows that the principal axis of stress is parallel to the grain direction. It also
shows that
f w = fsi f,=f„ f*» = (2:41)
The resulting strains are obtained from equation (2:26)
^bt+ltf) e * =i  (ir+W, e " =0 (2:42)
*sz
fsz
Figure 223. — Plywood in shear at 45° to the face grain direction.
From equation (2:27)
58
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
<
The resulting strain circle is shown in figure 225. The value of c is negative and there
fore the center of the circle lies to the left of the origin. Since e sw = 0, the direction of e w ,
and therefore the direction of the face grain, is parallel to the direction of the principal
axis of stress.
The modulus of rigidity at 45° to the grain direction {G is ) is defined as the shear
stress divided by the shear deformation, or
G iS =^=—. j (2:45)
We e ~e~
The associated direct strain
For E W = E X , e, =0, and the center of the strain circle coincides with the origin. Then
which is the relation obtained for isotropic materials.
I
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
59
*2.56ll2. Experimental stressstrain data. Figure 226 presents stressstrain curves
typical of those obtained in a few exploratory tests of plywood to which the stresses were
applied at 45° to the face grain direction and in which the grain direction of alternate
plies was at 90°. The types of specimen on which these curves were obtained are also
indicated in figure 226. For experimental stressstrain curves, see reference 226.
2.6. PLYWOOD STRUCTURAL ELEMENTS. The following formulas for
strength of plywood elements are applicable only when elastic instability (buckling)
is not involved, except in the case of column formulas. For cases involving buckling,
see section 2.70.
2.60. Elements (6 = 0° or 90°).
2.600. Elements in compression (6 = 0° or 90°). When a plywood prism is sub
jected to a direct compression load, the relation between the internal stress (/ c l) in any
longitudinal ply and the average P/A stress is given by the following equations:
Face grain parallel to applied load
P/A &) (2:47,
(Nl OS U3d 97) SSJVIS
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
61
Face grain perpendicular to applied load
PM (2:48,
The allowable stresses at the proportional limit F cpw and F cvx , or the allowable ulti
mate stresses F cuw and F eux are obtained from these equations, respectively, when the
stress at the proportional limit F CP or the ultimate crushing stress F cu from table 23,
whichever is required, is substituted for/ ( L. When more than one species is used in the
longitudinal plies, the species having the lowest ratio of F,. p /El and F, u /El must be used
in determining the correct allowables. For certain species and plywood constructions,
the compression allowables may be obtained from table 29.
*2.601. Elements in tension (6 = 0° or 90°). Under tension loads the fiber stress
at proportional limit for wood is, in most cases, very close to its ultimate strength. This
fact should be given careful consideration in the design of wood and plywood tension
members, and stress concentrations should be avoided. An equalization of stresses for
loads above the proportional limit cannot be assumed, as in the case of metal structures,
since yielding will be closely followed by complete failure.
The allowable ultimate tensile stress for a plywood strip (designated as F tU w when
the face grain direction is parallel to the applied load, and F tux when the face grain is
perpendicular to the applied load) is equal to the sum of the strengths of the longitudinal
plies divided by the total area of the cross section. The strength of any longitudinal ply
is equal to its area multiplied by the modulus of rupture for the species of that ply as
given in column 8 of table 23. For certain species and plywood constructions, the ten
sion allowables may be obtained from table 29.
*2.602. Elements in shear (0 = 0° or 6 — 90°). The allowable ultimate stress
F swx of plywood elements subjected to shear is equal to the sum of the shear strengths
of all plies divided by the total crosssectional area. The shear strength of any individual
ply in a direction parallel to that of its grain is the allowable shear stress parallel to the
grain (column 14 of table 23) multiplied by the crosssectional area of that ply. The
shear strength of any ply in a direction perpendicular to that of its grain can be taken as
1.5 times the allowable shear stress parallel to the grain (column 14 of table 23) multi
plied by the crosssectional area of that ply. Thus, two allowable shear stresses will be
obtained, one parallel to the face grain and one perpendicular to the face grain; but since
shear stresses are always applied equally in these two directions, the lesser value of the
two is the proper allowable stress to use. The ultimate shear stresses for certain species
and plywood constructions both parallel and perpendicular to the direction of the face
grain have been computed. The lesser of the two are given in column 20 of table 29.
A few exploratory tests indicate that the shear values of table 29 are applicable
to plywood made from veneers of approximately V nrinch thickness and that an increase
in strength may be expected from plywood made of thinner veneers. This effect is being
further investigated.
2.61. Elements (6 = any angle).
*2.6l0. Elements in compression (6 = any angle). Based upon the results of com
pression tests of a few species and constructions of plywood, the ultimate compressive
stress may be given by :
62
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
F cu6 F cuw qq° cuw Fcux) (2:49)
where :
6= angle between the face grain and the direction of the applied load in degrees.
F cu w = ultimate compressive strength of the plywood parallel to the face grain; from
formula (2:47)
Fcux = ultimate compressive strength of the plywood perpendicular to the face grain;
from formula (2:48).
*2.6ll. Elements in tension (0 = any angle). The ultimate tensile strength of ply
wood in this case is given by the formula:
F tu9 = — 1 (2 :50)
rcos 2 6 "1 2 , rsin* 0~i 2 . rsin 6 cos
where: F tU w and F tux = ultimate tensile strength of plywood parallel and perpendicular"
to the face grain direction, respectively, from section 2.601; and
F swx = ultimate shear strength of the plywood when the face grain direction is parallel
and perpendicular to the shear stresses, from section 2.602.
*2.6l2. Elements in shear (0 = any angle). The ultimate shear strength of ply
wood in this case is given by equations (2:51) and (2:52). When shear tends to place
the face grain in tension, equation (2:51) should be used. When shear tends to place
the face grain in compression, equation (2:52) should be used.
When face grain is in tension
y
(2:51)
 X
When face grain is in compression
v
(2:52)
For the special case of the face grain at 45° to the side of the panel, equations (2:51)
and (2:52) reduce to
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
63
(2:53)
(2:54)
*2.613. Elements in combined compression (or tension) and shear (0 = any
angle). The condition for failure of plywood elements subjected to combined stresses
in the plane of the plywood is given by the following equation. Formulas 2:50 to 2:54
are special cases of this general equation.
^)'+( / t)' + (fe)'' ■
where :
f w /F u , = ra,t\o of the internal tension or compression stress, parallel to the face
grain, to the allowable tension or compression stress in the same direction.
fx/F x = ratio of the internal tension or compression stress, perpendicular to the
face grain, to the allowable tension or compression stress in the same
direction.
fs w x/F s wx — ratio of the internal shear stress, parallel and perpendicular to the face
grain, to the allowable shear stress in the same direction.
In the use of equation 2 :55, it is necessary to first resolve the internal stresses into
directions which are parallel and perpendicular to the face grain direction.
In order to clarify the use which can be made of the combined loading equation 2:55,
the complete derivation of equation 2:50 is given. It is desired to find the allowable
tensile stress of a plywood element which is loaded as shown in figure 227.
Figure 227. — Orientation of plywood element for derivation of formula 2:50.
04
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Resolving stresses
ftw=ft cos 2 6
ft x =ft sin 2
fsw X =ft sin cos 6
Substituting these terms in the combined loading equation
the following is obtained:
Vft cos 1 6 1*  V f t sin 2 8 V  V f t sin cos ~~ 1
L P'tuw J [_ Ftux J _ F IWX J
Dividing through by /, and setting its value equal to the allowable tensile stress, F tu e,
gives equation 2:50, or
F tu9 = (2:50)
4
cos 2 6 1 2 p sin 2 6 " * r sin cos 6  8
Equations 2:51 and 2:52 may be derived in exactly the same manner. Experiments
indicate that equation 2:55 is conservative in the case of compression at angles to the
grain and that equation 2 :49 can be used.
2.614. Elements in bending. The apparent moduli of elasticity {E fw and E fI ) of
plywood beams in bending are given by the general formulas in section 2.5. When all
of the plies are of equal thickness and one species, these general formulas reduce to the
following forms :
For rotarycut veneer,
3ply;^=(+^) **HsK 1+ "s9 (2:56)
5ply; 2^=J§ (^+99) Z^=J§ (»+"f=) (2:57)
7ply; E fw =^ (99 f+m) E fx =^ (90+144 f) (2:58.
9ply: E fu ^ (®44 %+^ 85 ) EfI= W9 { 2 ^ + ^ 85 ( 2:59)
For quartersliced veneer, Et/El should be replaced by Er/El (sec. 2.13).
The bending stress in the extreme fiber of the outermost longitudinal ply is given by
the following formulas:
Face grain parallel to span
'^mi (B (2:60)
Face grain perpendicular to span
^ = 7^r(lt) cfor3  ply) • (2:61)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
65
'»=^(j7> Uother) (2:62)
Mc' /El
where :
c'= distance from neutral axis to extreme fiber of outermost longitudinal ply.
£" /x = same as E fx except that outermost ply in tension is neglected. E fx may be
used in place of E' fx in formula (2:62) with only slight error.
El is taken for the species of the outermost longitudinal ply.
The allowable bending stress at proportional limit (Fi,„) and the modulus of rupture
in bending {F bu ) are given in table 23.
**2.6140. Deflections. The deflection of plywood beams with face grain parallel or
perpendicular to the span may be obtained by using E fw or E fx in the ordinary beam
formulas. E' fx is used only for determining strengths in bending and not the deflection.
For plywood beams with face grain at an angle 6 to the direction of the span, the effective
modulus of elasticity to be used in the deflection formula is given by the equation :
E = E fw cos*Q+£ sin 2 6 cos 2 V+E, x sin* 6 (2:63)
o
when
(1) The loading is constant across the width of the beam at any point in its span.
(2) The beam width is sufficient to cause the. deflection to be constant across the
beam at any point in the span.
(3) The beam is held so that it cannot leave the supports.
There are no methods available by which the bending stresses in plywood beams
may be calculated when the grain direction of the face plies is other than parallel or per
pendicular to the span. (ref. 224.)
*2.6l5. Elements as columns. The allowable stresses for plywood columns are
given by the following formulas:
Long' columns
■p^_ 0.85 ir Eju, ££ ace g ram p ara ll P l to length) (2:64)
0.85 7T * E
fx
(face grain perpendicular to length) (2:65)
(L'/ 9 ) cr =3,55yJ E
F c u w
or 3.55 yjy^ respectively
Short columns
''['i (2:66)
where :
K = (L'/ P ) cr
Fcu — Fcuw when face grain is parallel to length.
= F CUX when face grain is perpendicular to length.
66
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS
67
2,820
3,080
2,700
2,350
2,710
2,460
3,190
3,520
2,920
3,070
2,750
2,260
2,610
2,440
3,210
3,420
2.900
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2,720
2,260
2,540
2,400
3,170
2,120
2,700
2,140
2,110
2,190
2,040
2,870
3,300
2,400
2,940
2,360
2,260
2,440
2,280
3,100
3,420
2,510
3,020
2,400
2,200
2,540
2,380
3,170
1,430
1,160
1,130
1,110
1,500
1,300
1,100
1,810
1,420
1,200
1,160
1,140
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1.S40
1,420
1,210
1,170
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1,500
1.310
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4,270
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4,550
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9,300
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5,100
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6,900
8,230
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6,160
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6,110
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2,180
2,930
2,250
2,320
2.310
2,130
3,160
3,600
2,510
3,340
2,560
2,610
2,660
2,400
3,600
3,810
2,650
3,530
2,710
2,610
2,820
2,610
3,800
4,480
4,120
4,020
2,900
3,340
3,340
4,440
4,030
3,990
3,710
3,590
2,610
2,980
2,980
4,000
3,810
3,770
3,530
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2,820
2,820
3,800
1,640
2,200
1,690
1,740
1,730
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2,530
2,700
1,880
2,510
1,920
1,960
1,850
2,880
2,860
1,990
2,650
2,030
1,960
2,120
1,900
3,040
3,360
3,090
3,020
2,180
2,500
2,500
3,550
3,030
3,000
2,790
2,700
1,960
2,240
2,240
3,200
2,860
2,830
2,650
2,550
1,900
2,120
2,120
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752
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879
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877
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1,080
1,070
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784
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1,020
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5 053
3 929
3.860
4 331
3.393
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11.307
6 951
9 397
7 325
7 340
8 402
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19.224
11 726
15.704
12 254
11 287
14.387
11.277
15 569
20 60
15.47
15 43
11 85
15 43
15 43
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30 94
30 89
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230
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1,190
1,180
1,190
1,210
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS
69
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70
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS 71
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. lllll.llISiSilllSll§l!
fllilillilllllll
Sill
&. &.
m
fa
PQ PQ
&, fa
m
fa
eq
fa
fa
CO
fa
pa
<
fa
CQ
fa
fa
m
fa
CQ
fa
CQ
fa
Birchyellowpoplar
1

i
i
Yellowpoplaryellowpoplar

Birchbirch
Birchyellowpoplar
)
Mahoganyyellowpoplar '
Yellowpoplaryellowpoplar

Sweetgumyellow poplar
1 1
S
I
1
=*
2
2
"5
2
<™
2
»
2
2
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
! \§\sri
3,470
2,620
3,040
2,200
2,290
2,570
2,280
3,190
1!
i
I
3,370
2,400
2,980
2,350
2,240
2,500
2,310
3,150
1
I
1,830
1,300
1,210
1,150
1,130
1,550
1,240
1,140
Ultimate
strength in
1
1
8 § §
' S § 1  i 1
r' .re" ■#" «
1
I 1 I S 8 i J 1
.re .c r» .re" .re .re'
crushing
strength
s
hi
3,720
2,580
3,450
2,010
2,550
2,760
2,550
3,720
1
3"
as If
1 1 1 1 1 I
sf M CO' N of 5,
! I S
Fiber stress at!
proportional
1 imit
2,800
1.930
2,590
1,960
1,910
2,070
1,910
2,970
I
2,930
2,430
2,700
1,970
2,010
2,170
? 1
"3
J
a
1 M
a
65
1.050
927
768
751
765
759
761
1,040
Static bending
Moment for
modulus of
rupture
ill
S:
Mi
157.5
93.4
121.0
94.6
92.5
117.9
92.4
120.0
"i —
& 
o
I n.lb.
per
in. of
width
213.5
211.6
162.8
159.U
125.3
159.8
159.8
161.4
ii
111
In.lb.
per
in. of
width
i 1 I 1 i 111
iir
1»
g
In.lb!
per
in, of
width
130.8
129.7
123.5
121.3
82.6
103.3
103.3
112.2
i
8
s
m
■f. i • i i , i i i N i
■a
&?
§
1 &s
1 S.I II 11. s
3
1 M
  1 S I ' S " 8 I
I
m
(15
per
mois
ture) 2
1,480
1.120
1.155
1.020
.900
1.155
1.020
1.155
si
s
1 1 1 1 1 i i i i i I i 1 1 § i I i i I i 1 1 i
«;E23pa=Qqa««
1
'o
a
w
Nom
inal
thick
ness
— si
>— <
.375
.375
.375
.375
.375
.375
.375
.375
«
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
73
mum
2§2ggg
3 «■ £ «• S s s s
SSS999S9
IllIll!!
IHISIH
SSI I
11111115
N rH O) rH «
II:
399
ii
ci CO
IlliiiSl
•4 ^
ooH«o;iflo:o
CO of cm' of of « N of
59393999
99599999
ii
3 S 3393 5
99555959
SillllSi
N  c^" J _J rH I
II
Ills!
of of of Of CO'
iiiiiisi
n « n o o a x
IBsrlSsss
SISolsllS
SSIlBlSi
of of of of of of S 3 ol S" of of of of co'
rH h" rH rH rH* rn' rH rH rH " rH  rH rH rH rH rH _
II!I!!!I ISBSSSSi
I 1 1 1 ill:
lisllll
55595151 51999991
Slilllll IllllSiS
leSSIIKS StSMISS
Of rH Of rH' rH" rH rH of of of of '  h' rH  of
III955I5
iSHSUl
1 1 ! * i 1 1 s
rH' rH' rH rH rH ri rH rH
OOOOOggO
3 S S I 3 5 5 3
2 S? § 2
o * "f o
00 CD CD 10 <
IIS
co of co" of of of of co"
!!!!!§!!
Of of rn" rH ,H rH of
iiiiiiii
rH" rH"
missis
1
SSssISirl
5SS33533
pilllll
2 533 HIS
ggtsmg
&H
I
3SSS3SS9
11111111 lilliili
11111111
co of of of of of of co"
ISIS 5 111
lllllglr!
r'
I i g 1 1 g S I
3S335332
llllllil
lilliili
74
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
I
1
s
Oh
I
a
&3
Ultimate
strength in
shear
!
1
st{ !!III!!SI!1!SI!§
i
per
sg. in.
3,230
2,510
2,900
2,190
2,160
2,400
2,190
3,060
3,230
2,510
2,900
2,190
2,160
2,400
2,190
3,060
i
1
Lb.
per
sq. in,
1,800
1,370
1,190
1,140
1,120
1,530
1,270
1,130
1,800
1,370
1,190
1,140
1,120
1,530
1,270
1,130
Ultimate
strength in
tension
i
OS
Lb.
per
sq. in.
7,050
5,300
5,270
4,590
4,140
5,270
4,590
5,230
§§§§!!!
9
I
00
Lb.
per
sq. in.
8,450
6,130
6,330
5,420
4,950
6,330
5,420
6,270
ISSSIilS
]1
strength
i
Lb.
per
sq. in.
3,500
2,750
3,260
2,400
2,400
2,590
2,390
3,510
8S2
m <n" m* n" « «" 3 m
1
so
Lb.
per
sq. in.
4,130
3,180
3,800
2,840
2,830
Ill
4,130
3,180
3,800
2,840
2,830
3,060
2,820
4,090
Compression
Fiber stress at
.1
1
&,
Lb.
per
sq. in.
2,630
2,060
2,440
1,800
1,800
1,790
2,810
2,630
2,060
2,440
1,800
1,800
1,940
1,790
2,810
1
&.
s
Lb.
per
sq. in.
3,100
2,390
2,850
2,130
2,120
2,290
2,120
3,270
3,100
2,390
2,850
2,130
2,120
2,290
2,120
3,270
Modulus of
CO
IglllllS
1,000
lb. per
sq. in.
1,110
910
810
811
809
803
807
1,090
1,110
910
810
811
809
803
807
1,090
Moment for
modulus of
rupture
it*
s
In.lb.
per
in. of
width
779
732
604
596
457
583
584
598
§§133813
Paral
lel 3
o
In.lb.
per
in. of
width
1,030
955
791
795
607
774
776
785
1,460
1,350
1,120
1,120
857
1,090
1,100
1,110
;ic bending
Moment for
fiber stress at
[l
e
h
In.lb.
per
in. of
width
634
585
600
603
400
501
502
546
§S3§§SS£
i
5
5
j
8
IJi siiiiiis
SUSHIS
&
CO
1,000
lb. per
sq. in.
1,160
1,070
840
844
848
841
843
1,130
§§133333
3.96
3.07
3.09
2.75
2.56
3.09
2.75
3.09
j]
CO
= ©
iliiiii
s
s
Birchyellowpoplar
Mahoganymahogany
Mahoganyyellowpoplar
Yellowpoplaryellowpoplar
sweetgumsweetgum
Sweetgumvellowpoplar
DouglasfirDouglasfir
Birchbirch
Birchyellowpoplar
Mahoganymahogany
Mahoganyyellowpoplar
Yellowpoplaryellowpoplar
feweetgumsweetgum
Sweetgumyellowpoplar
1
Nom
inal
thick
ness
4 pill!!!
2222222S
SSS2SSSS
11
if
1
11 I
lit
1
llli
'Sjj.3
' CM ^ 82
111
I ill
Ir
Willi
 2
J2 o
o d :
3 •s
If
t!
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
75
Table 210. — Budding constants for plywood 1
THREEPLY
Shear
Compression
Face grain
angle
45°
0°
0°
90°
Face grain in
tension
Face grain in
compression
0°
and
90°
90°
45°
Nominal
thickness
b'/a
00
b'/a
CK.) oo
b'/a
(*.) oo
b' /a
b'/a
b'/a
(#c) 00
b'/a
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(id
(12)
(13)
(14)
Inch
0.035
.070
.100
.125
.155
.185
60
.80
.75
.88
.94
.95
2.13
1.79
1.85
1.70
1.65
1 .64
2.05
2. 11
2 10
2 13
2.14
2.14
0.60
.68
.66
.71
.72
.73
. 57
.78
.73
.87
.93
.94
0.95
1.06
1 03
1 10
1 12
1 13
3.50
3.34
3.38
3 27
3 22
3 22
1 74
1.72
1.72
1 71
1.70
1.70
1 88
1 62
1 67
1.55
1 50
1 50
6.71
.82
.80
.87
.89
.90
0.53
.62
.60
.65
.67
.68
0.86
1 08
1.03
1 17
1.23
1.24
84
.91
.90
.93
.94
.94
FIVEPLY
160
1
25
1
42
2
13
.83
1
29
1
26
2
91
1
66
1
31
1
02
.77
1
49
.97
190
1
35
1
36
2
12
.87
1
41
1
30
2
81
1
64
1
26
1
04
.80
1
56
.98
225
1
37
1
35
2
11
.88
1
43
1
31
2
79
1
63
1
25
1
05
.81
1
57
.98
250
1
30
1
38
2
12
.85
1
35
1
28
2
86
1
64
1
28
1
04
.79
1
53
.98
315
1
29
1
39
2
12
.85
1
34
1
28
2
.87
1
65
1
29
1
03
.78
1
52
.98
375
1
48
1
28
2
08
.92
1
57
1
36
2
66
1
60
1
19
1
.08
.84
1
64
.99
SEVENPLY (All plies oj equal thickness)
Any I 1.40  1.32  2.10 \ .89 I 1.46 I 1.32 I 2.75 I 1.62 I 1.23
NINEPLY (All plies oj equal thickness)
Any  1.52  1.26  2.06  .94  1.63  1.37  2.60  1.59 I 1.17
ELEVENPLY (All plies of equal thickness)
Any  1.59 I 1.22  2.03  .96  1.72  1.40 I 2.52 I 1.58 I 1.14  1.10
1.06
1.09
1.59
.86 I i.e
1.70
.99
.99
1 The buckling constants listed in this table correspond only to the plywood thicknesses and constructions listed in table
29 that correspond to ArmyNavy specification ANNNP51 lb, (Plywood and Veneer; Aircraft Flat Panel). The values in
this table were computed as follows: For each construction given in table 29 a value of — — was computed from col
Ef„. +Ef*
umns 5 and 6 of table 29. These values for each thickness were averaged and the average values were used in entering figures
237, 238, 239, and 240, from which the values of this table were obtained. For a more exact determination of these buckling
constants or to determine the buckling constants of a plywood construction different from those specified in ANNNP51 lb,
see section 2.701.
76
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
2.7. FLAT RECTANGULAR PLYWOOD PANELS.
2.70. Buckling Criteria.
2.71. General. When buckling occurs in plywood panels at loads less than the
required design loads, the resulting redistribution of stresses must be considered in the
analysis of the structure. The buckling criteria in this section are based on mathematical
analyses and are confirmed by experiments for stresses below the proportional limit.
Visible buckling may occur at lower stresses than those indicated by these criteria, due
to the imperfections and eccentric loadings which usually exist in structures. Experi
ments have indicated, however, that the redistribution of stresses due to buckling corre
sponds more closely to the degree of buckling indicated by these theoretical criteria than
it does to visible buckling. These criteria can, therefore, be used in various parameters
for plotting test results or design allowables against the degree of buckling, and to com
pute the degree of buckling in a structure. This is done in sections 2.72 and 2.760.
Since the mathematical analyses are based on the assumption of elastic behavior,
these criteria cannot be directly applied when the stresses are above proportional limit.
The behavior at such stresses has been investigated experimentally for some cases, as
described in sections 2.72 and 2.760.
*2.710. Compression or shear. The critical buckling stress of flat rectangular ply
wood panels subjected to either uniform compression or uniform shear stresses is given
by the following general formulas.
El is for the species of the face plies, from table 23.
K c and K s are factors depending on the type of loading, the dimensions of the panel,
the edgefixity conditions, and Poisson's ratio. K c and K s are determined by the following
methods.
Let a be the width of a rectangular panel of infinite length of which a portion of
finite length b is being considered.
The mathematical treatment of buckling constants presented in this section has been
based on the assumption that the compression load is always placed on the edge having
dimension o. In a panel loaded only in shear a dimension of either edge may be taken
(2:67)
(2:68)
where :
STRENGTH OF N OOD AND PLYWOOD ELEMENTS
77
as a, and the panel shall be considered as a p = 0° ease when the face grain is perpendicular
to the edge having dimension a and as a £=90 o case when the face grain is parallel to
the edge having dimension a. (Fig. 228.)
/3=0°
Figi re 228. — In panels loaded in shear, a may be a dimension of either edge. For (J = 0°, face grain is
perpendicular to a; for (i = 90°, face grain is parallel to a.
One method of obtaining A' s or K c is by the use of figures 229 to 234 as explained
in section 2.711. Approximate values of A s or K c suitable for ordinary purposes may be
obtained by correcting A s00 or K cO0 values in table 210 for panel size by means of
b' b
figures 235 or 236. In using these figures — is first obtained from table 210 and
i ; b'
computed. For a more exact determination of A s or K c or to determine these buckling
constants for a plywood construction different from those specified in ANNNP511b
or figures 229 to 234, calculate — — in accordance with section 2.52, read K s0 r
or A (00 and b'/a from figures 237 to 240 and correct for panel size by means of figure
2 35 or 236.
**2.711. Combined compression (or tension) and shear. Panel edges simply
supported. The analytical method of determining the critical buckling stresses for
rectangular panels subjected to combined loadings is quite complicated, and only the
graphical solutions for a few types of plywood construction are given in figures 229
to 234.
When the plywood construction being used is not the same as any of those illustrated,
its buckling constants may be obtained by a straight line interpolation (or extrapolation),
E fw
on the basis of — — — — , of the buckling constants for two plywood constructions whose
E
values of the ratio ^— are fairly close to that of the plywood under consideration.
V TP
&fw+&fx
The values of these ratios for the plywood constructions considered in figures 229 to
234 may be calculated with sufficient accuracy by assuming Ay = 0.05 El
These figures apply to panels of infinite length and values of the buckling constants
from the curves must be corrected for actual panel length. Values of the shear constant
78
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
iv s oo and the compression constant K cX are indicated on the vertical and horizontal
axes, respectively. The points at which the curve crosses these axes give the values of
A%oo or /Ceo at which buckling will just occur in a panel of infinite length in either pure
shear or pure compression. The particular combination of stresses represented by each
of the four quadrants is shown by the small stress sketches. Buckling will occur under
these combined stresses whenever the location of a point K s(Xl , K c0 o, lies on or outside
the curve.
The curve marked b'/a is the ratio of half the wave length (b') of a buckle in an
infinitely long panel to its width (a). This ratio is to be used in conjunction with figures
235 to 240 in obtaining the correction factors for panels of finite length to be applied
to K s0 o.
The curves in figures 229 to 2 34 marked y give the slope of the panel wrinkles with
respect to the OX axis indicated on the stress sketches.
The procedure in the use of these figures is as follows:
(1) From the analysis the shear stress (f s ) and the compression (/<.) or tension stress
( — fc) acting on a particular plywood panel will have been calculated.
(2) Determine the ratio f s /f c and, on the figure giving the same plywood construc
tion and angle £}, draw a line through the origin having a slope (positive or negative)
equal to this ratio. When the plywood construction is not the same as that given in the
figures, this procedure for determining the buckling constant will have to be run through
on the two most similar constructions and an interpolation of the results made on the
basis of — — ^ — :
E fuj+Efx
(3) The point at which the constructed line crosses the curve gives the critical
buckling constants K sX and K cOD at which an infinitely long panel will just buckle when
subjected to the same ratio of shear to compression that exists on the panel in question.
(4) Read the value of b'/a for the point on the b'/a curve which is obtained by
projecting horizontally from A' s0 o determined in step (3).
(5) From the panel dimensions compute b' and b/b'.
(6) Figures 235 to 240 will give the ratio of K s /K sX from which the value of
K s can be computed (A' s is always taken as positive).
(7) The critical buckling shear stress (F Scr ) may then be determined by equation
2:68. This represents the maximum allowable shear stress which the panel in question
can sustain without buckling when subjected simultaneously to a compressive stress
equal to that given in step (1).
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
79
4
SCALE fOR % AND T
SCALC FOR % ItID 7
(c) (J I
?PLY(ll)Q 30' 2P L Y (1:1) 45'
Figure 229. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. £1 = angle between lace grain and direction of applied stress.
Twoply construction.
80
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
(tj If)
Figure 229. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
(combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress.
Twoply construction, (continued)
fa] (b)
3PL1 (I N)Q0~ 3PLY (l l l)/3* >i'
Figure 230. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. (i = angle between face grain and direction of applied stress.
Threeply construction.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
81
Figure 230. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported, = angle between face grain and direction of applied stress.
Threeply construction, (continued)
82
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Figure 230. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported, p = angle between face grain and direction of applied stress.
Threeply construction, (continued)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS 83
(kl Inn)
3PLY (l*:l)/345' 3PLY (l:2:i)/S=0"
I I, i
SCALE FOB % OHO y
3
r i\
f
"
~ . ■
X
0
X
— 1
5
s
I,
4
y
' 1
0
—i
 3
— 4
S
iCAlC FOI>%AKD~r
(n) (PI
3PLY (l:Z i)/3 75 3PLY (lit) W
Figure 230. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress.
Threeply construction, (continued)
84
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(a)
3ply(i z i)b o
(b)
— 3
A 2
s
\
Oi

f
Milk
1 1
Y
<M
o i
V
1
/
T
— z
/
l
s
3
V
— i
tOll
JCAL £ FOR % AHO 7 y
Figure 231. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading with edges clamped. @ = angle between face grain and direction of applied stress.
Threeply construction.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
85
Figure 231. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading with edges clamped. £ = angle between face grain and direction of applied stress.
Fiveply construction, (continued)
86
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(C) (ct)
5PLY (l:N:l:l)a30 w 5PLY (MWOMST
Figure 232.— Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. = angle between face grain and direction of applied stress.
Fiveply construction.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
87
Figure 232. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. £ = angle between face grain and direction of applied stress.
Fiveply construction, (continued)
88
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
(k) cm)
SPLY (l&a&l) 04£ 5PLY(l:iWl)0* 60*
Figure 232.— Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. = angle between face grain and direction of applied stress.
Fiveply construction, (continued)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
89
r
As
Y
X
j
—
Y
<
— /
f
>
X
•5
h
•
.'
 1
X
 2
Y\
<
Ce
'3
*[ l
1
d

4
I
5
10 12
scau roe % and j
 J
.
Y
1
» 1
0
V
f
m
' 1
5
4
1
Y,
/
r'
L
If
/
3
•4
\
S
/ ,, 1 i
imc rm %/m 7 i
5PLY{l 11 Zl)/3 15'
SPLY(l*:?i:l)/390'
Figure 232. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress.
Fiveply construction, (continued)
(a)
9PLY (ill III I I l)6 0'
ii
3
s
Y
n
4
It
7 '
Y
II
H
'1
11
— /
j '
(1
M
i
1
I,
Z
)
Y\
/
ih
mm
nltim
\>
."if
X
—z
y
1
III
4
%
—3
9 J
1
ill
>
— 4
—5
10 12
scalc route, />nr> r
(b)
9PLY(l 1 1 1 1 1 1 1 15'
Figure 233. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. ^ = angle between face grain and direction of applied stress.
Nineply construction.
90
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
'a (f)
9PLY(llillll.li)fi to <3PLY (l I I l lI l l 75'
Figuee 233. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported, (i = angle between face grain and direction of applied stress.
Nineply construction, (continued)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
91
\
— 4
I
iiiii
I
X *
=ji
^dl X
Y
iR3l
HIM
\

mil
— Z
\
— /
X
inn
\
J
!
1
\m<
J
tm
 01
Mill
y
Z
MM
in
Mil _
1
— Si  ~~
y
 3
 4
/ 0,1 2.
SCALE FOB % AND r
if)
9PlY thbl:l:l:l:IH;l)a*tO'
I .1 2
JCAl£ FOB % A/IP *■
(i)
lPlY(l:ll:l 1:1:1.1 l)a4S'
(h)
9PLY (l Z Z I 2 Z Z Z l)j3 »'
\
— 4
Itttt
l"M
mi
— J
I
— L
" Y
)
— 6 1
<
1 1
1
t
r
L
MM
hh
MM
o (
Hill
 3
i(Alf FOB % 6HD
(J)
S Pit (i Z 1:2 Z Z Z Z l)a 9°'
Figure 233. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. @ = angle between face grain and direction of applied stress.
Nineply construction, (continued)
92
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Figure 234. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported. @ = angle between face grain and direction of applied stress.
Infiniteply construction.
Figure 234. — Curves of critical buckling constants for infinitely long rectangular plywood panels under
combined loading. Edges simply supported, p = angle between face grain and direction of applied stress.
Infiniteply construction, (continued)
94 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
6
9 8 7 6 5 4 3 2
io\ 1 — —i r= — I i i i i i i — i 1 1 r
O 0.1 01 0.3 OA 0.5 O.b 0.7 0.6 <?.9 1.0 I.I 1.2 1.3 I A 1.5
A
b'
Figure 235. — Corrections for panel size when (3 =0°, 45°, or 90° when the panel is subjected to shear stress.
967b545Z
10
06
0.4
/
/
/
+
s
^^^^^
N
c
y
§r
' / y
f / //
/'
//.
— v/y j
firsts
OZ 04 0.6 OS 10 IZ 1.4 IA
b
T'
Figure 236. — Corrections for panel size when panel is subjected to compression. (3=0° or 90° is a
computed curve. (Ref. 212.)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
95
 rf
V
ass o.b as oi 075 a a oss o.9 tm i.o
Figure 237. — Buckling of infinitely long plates
of symmetrical construction under uniform shear.
Edges simply supported. The constant A' s oo plot
E fw
ted as a function of the ratio .
Ef W \Ef X
z.o
1.6
1:6
1.4
1. 1
%
^J.O
0.8
O.i
0.4
0.2
A.
JU 0.55 0.6 065 0.1 015 0.8 0.65 0.9 0.95 1.0
Lb*
Figure 239.— Buckling of infinitely long plates
of symmetrical construction under uniform com
pression. Edges simply supported. The constant
E
Kctx plotted as a function of the ratio 
fx
■FACt
,.n>
V IN,
HI ■
SI0H
<
OS OSS Qi 0&f> 07 075 08 OSS 0$ 09$ iQ
Figure 238. — Buckling of infinitely long plates
of symmetrical construction under uniform shear.
Edges simply supported. The constant b'/a plot
Ef W
ted as a function of the ratio .
E/ w \Ef X
2V
1.8
16
1.4
II
6
Oi
4
2
Efw+E JX
OS 055 Ob 065 0.7 75 06 06S 09 095 W
Figure 240. — Buckling of infinitely long plates
of symmetrical construction under uniform com
pression. Edges simply supported. The constant
Ef W
b'/a plotted as a function of the ratio .
E fw +E fx
96
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
2.72. Allowable Shear in Plywood Webs.
2.720. General. Beams are required to have a high strengthweight ratio and, there
fore, they are generally designed so that they will fail in shear at about the load which
will cause bending failures. A higher strengthweight ratio is usually obtained if the
beams fail in bending before shear failure can occur.
Plywood when used as webs of beams is subjected to different stress conditions from
those when it is used in simple shear frames. It is essential, therefore, that tests to deter
mine the strengths of shear webs be made upon specimen beams designed with flanges
only sufficiently strong to hold the load at which shear failure is expected. Plywood
webs tested in heavy shear frames with hinged corners will give shear strengths that are
too high for direct application to beam design.
In any case where buckling is obtained, the stiffeners must have adequate strength
to resist the additional loads due to such buckling, and the webs must be fastened to
the flanges in. such a manner as to overcome the tendency of the buckles in the web to
project themselves into this fastening and cause premature failure.
*2.721. Allowable shear stresses. The allowable shear stresses of plywood webs
having the face grain direction at 0°, 45°, or 90° to the main beam axis may be obtained
from figure 241.
The direct use of figure 241 for any type of beam having 45° shear webs has been
verified by numerous tests of I and boxbeams. A few exploratory tests of beams having
0° and 90° plywood shear webs has indicated that the allowable ultimate shear stresses
obtained for these constructions by using figure 241 are conservative. Until sufficient
additional tests have been conducted to establish a more rational method of determining
the allowable ultimate shear stress for plywood shear webs in which the face grain makes
an angle of 0° or 90° to the longitudinal axis of the beam, values obtained from figure
241 should be used.
Plywood shear webs of 45° are more efficient than 0° or 90° webs.
The designer is cautioned that box beams may fail at a load lower than that indi
cated by the strength of the webs as shown in figure 241, because of inadequate glue
areas of webs at stiffeners or flanges. Such premature failures result from a separation
of the web from the flanges or stiffeners. Additional information for guidance in stiffener
design is presented in reference 27.
Figure 241 contains a parameter a/b in the form of a family of curves. The a/b = l
curve represents a spacing between stiffeners just equal to the clear depth between flanges.
The curves below a/b = 1 should be used for the design of shear webs of beams whose
stiffener spacing exceeds the clear distance between flanges. The upper set of curves
should be used for the design of beams whose stiffener spacing is less than the clear dis
tance between flanges.
Although, in a strict interpretation, the curves in figure 241 apply only to plywood
webs of beams, it is believed that they may also be used to calculate the shear strength
of other types of plywood shear panels (such as in wing skins, or fuselage coverings
having little or no curvature) provided certain precautions are taken. If any edge of a
panel is not rigidly restrained against movement in its own plane, the lowest curve
(a/b = 0.2) should be used. An example of this may be a plywood panel in the wing
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
07
covering at the inboard end of an outer panel where 1 the end rib does not afford a rigid
span wise support to the edge of the panel. The shear strength of a panel that is rigidly
restrained along all edges in its own plane may be determined by use of the o/h = 1.0
curve. A panel whose edges are entirely within a larger plywood sheet, or a panel that
is restrained on one or more sides by a heavy member, such as a beamflange, and on
all other sides by a continuation of the plywood, will fall in this group.
Further tests and studies will be made to ascertain if these applications of the curves
in figure 241 can be made in addition to its use for the design of plywood shear webs
of beams.
2.722. Use of figures 241 and 242. The abscissa of figure 241 is the ratio a/a
where « = either clear distance between flanges or clear distance between stiff eners
(sec. 2.701).
fl = the width of a hypothetical panel of length h which will buckle at a shearing
stress of F»$.
The procedure to be followed in the use of figures 241 and 242 is as follows:
(1) Knowing the panel dimensions a, b, and t and the plywood species, read the
values of F s o, K so o , and b'/a from tables 29 and 210. For plywood species and construc
tions not listed in tables 29 and 210 F sg may be calculated from equations in section
2.612 and A~ s0 o and b'/a may be read from figures 237 and 238 once E fw and E fx are
determined by test or from equations in section 2.52. K sX and b'/a may also be read
from the intercepts of figures 229 and 234 if desired. (Sec. 2.702.)
(2) Calculate a/6 and a/t.
(3) Calculate b/b' and read K sO0 /K s from figure 23.5. Calculate K s .
(4) From figure 242, read a/a as follows: (or a may be calculated from equation
2:69 if preferred).
(a) Draw line (1) connecting the appropriate El (for species of face plies),
and F s q.
(b) Pivot at scale (1) (2) and draw line (2) to the value of K s determined in
the third step.
(c) Pivot at scale (2) (3) and draw line (3) to the value of a/t found in the
second step.
(d) Read the value of a/a from the intercept on the a/a scale.
(5) The allowable shear stress (F„) for the web can then be obtained hi terms of
Ff/F a o from figure 2^41. (For a/a values greater than 4.0, the a/b curves may be ex
trapolated as straight lines to meet at a point corresponding to a/a a = 10 and F s /F s e =0.2.
98
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
99
100
ANC BULLETIN — DESIGN OP WOOD AIRCRAFT STRUCTURES
*2.72 3. Buckling of plywood shear webs. In connection with shear web tests on
various types of beams, it was observed that for plywood webs in the a/a range of
less than 1.2, buckling was of the inelastic type which often caused visible damage soon
after buckling and sometimes just as the buckles appeared for those webs designed to
fail in the neighborhood of F s e No accurate criteria can be presented at this time but
the designer is cautioned to avoid the use of webs that may be damaged by buckling
before the limit or yield stress is reached. The buckling curve established by these
tests is shown in figure 241. Additional information on buckling of plywood shear
webs is given in Forest Products Laboratory Mimeograph 1318B (Ref. 28.)
2.73. Lightening Holes. When the computed shear stress for a full depth web of
practical design is relatively low, as in some rib designs, the efficiency, or strength
weight ratio, may be increased by the careful use of lightening holes and reinforcements.
General theoretical or empirical methods for determining the strength of plywood
webs with lightening holes are not available, and tests should, therefore, be made for
specific cases. The effects of lightening holes in typical rib designs are discussed in
N.A.C.A. Technical Report 345 (ref. 223).
*2.74. Torsional Strength and Rigidity of Box Spars. The maximum shear
stresses in plywood webs for most types of box spars subjected to torsion may be
calculated from the following formula:
(2:70)
b' t(C'2b')
where:
t = thickness of one web.
b'=mean width of spar (total width minus thickness of one web).
C = average of the outside and inside periphery of the cross section.
The allowable ultimate stress in torsion of plywood webs is determined as in
section 2.721.
The torsional rigidity of box beams up to the proportional limit, or to the buckling
stress (whichever is the lesser) is given by the formula:
(i ±Gtb' T (C'2b')* i2:71)
2.7 5. Plywood Panels under Normal Loads.
2.7 50. General. When rectangular plywood panels, which have the face grain
direction parallel or perpendicular to the edges, are subjected to normal loads, the
deflections and in some cases the stresses developed, are given by the following
approximate formulas. If the maximum panel deflection exceeds about onehalf its
thickness, the formulas for large deflections will give results which are somewhat more
accurate than those given by the formulas for small deflections.
STRENGTH OP WOOD AND PLYWOOD ELEMENT
1(11
2.751. Small deflections.
(a) Uniform load — all edges s
imply supporte*
(2:72)
where:
\o = deflection at center of panel.
p = load per unit area.
a = width of plate, (short side)
K, = constant from figure 243 (a).
The maximum bending moment at the center of the panel on a section perpendicular
to side a may be obtained from figure 243 (b). The maximum bending moment on a
section perpendicular to side b is given by the same curve, provided a and b, and Ex and
Eg are interchanged in the abscissa, and a is replaced by b in the ordinate. The
corresponding stresses can be calculated from the formulas given in section 2.614.
(b) Uniform load — all edges clamped.
to = 0.031 A'„
2 Eft
(2:73)
where:
Ki= constant from figure 243 (a).
(c) Concentrated load at center — all edges simply supported.
(2:74)
where :
A's = constant from figure 243 (a).
2.752. Large deflections.
(a) Uniform load — all edges simply supported.
The relation between the load and deflection is given by the formula:
p = K i E L w j+A' 5 E L w a s —
(2:75)
where :
Ki and K 5 are constants whose approximate values are given in table 211.
E L is taken for the species of the face ply.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
103
The maximum bending moment at the center of the panel can be calculated from
the following approximate formula provided the length of the panel exceeds its width
by a moderate amount:
M max . = Xi Ei Wo p~2 (long narrow panels only) (2:76)
where:
X x = constant from figure 243 (c).
Although the edge support conditions are taken as simply supported, it is assumed
that the panel length and width remain unchanged after the panel has been deflected.
Therefore, in addition to the bending stress, there will be a direct tensile or membrane
stress set up in the plane of the plywood, and the total stress in any ply will be the
algebraic sum of the bending stress and direct stress in that ply. The maximum total
stress will occur in the extreme fiber of the outermost ply having its grain direction
perpendicular to the plane of the section upon which the moment was taken; the bend
ing stress being calculated from section 2.62, and the direct stress from section 2.601
after first determining the average direct stress across the section from the formula:
ftUi ) = 2.55 E n (—) (long narrow panels only) (2:77)
(b) Uniform load — all edges clamped.
The loaddeflection relation, formula 2:75, will also apply to this case provided
Kg and Ki from table 211 are substituted for and K$, respectively. The maximum
total stress may also be determined as outlined in (a) above, provided X2 from figure
243 (c) is substituted for Xi in formula 2:76.
2.76. Stiffened Flat Plywood Panels.
*2.760. Effective Widths in Compression. Because of the edge restraint afforded by
the stiffeners in stiffened panels, the ultimate stress or the fiber stress at the proportional
limit may be greater than the critical buckling stress of the sheet between stiffeners.
For convenience it is assumed that the sheet, which is under a variable stress, can be
replaced by effective widths acting in conjunction with the stiffeners at the same deforma
tion (but not necessarily the same stress). The remaining area of the sheet is considered
as being ineffective. The total effective width of sheet for any stiffener is made up of
increments w (measured from the outside edges of the stiffeners) plus the width of the
stiffener (see sketch on fig. 244).
104
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Table 2—11. — Values of constants in the approximate deflection formulas for plywood panels under normal
loads 1
Panel construction 2
Uniform load all edges
simply supported
Uniform load all edges
clamped
(6 la)
Ki
Ke
(b/a)
K'i
A'r
3ply, = 0°
1
1.5
2.0
>3.0
>1
(see (
1.7
.9
. 5
= 90°)
5.9
4.7
4.7
1.0
2.0
>3.0
(see i
3.6
2.5
» =90°)
6.0
7.0
= 90°
0.3
13.3
1.0
>2.0
1.0
2
>3
1.0
>2
33.3
32.0
27.9
19.2
5ply, 0=0°
=90°
1.0
1.5
>2.0
1.0
>1.5
(see t
2.4
1.5
6.2
5.0
= 90°)
6.5
6.0
12.3
10.0
(see (
8.3
7.9
28.7
26.5
1 =90°)
8.2
9.4
17.7
15.5
1 The values given in this table are for spruce plywood, all plies of equal thickness, but they may also be considered
applicable to plywood of other species and of the same constructions. For plywood made of more than five plies or of
unequal ply thickness, the above table may be used as a rough guide in arbitrarily selecting values of these constants.
 is the angle between the face grain direction and side b of the panel.
LEGEND'
A AVERAGE STRESS IN PLATE AT PROPORTIONAL LIMIT r PROPORTlONALLIMlT STRESS Of MATERIAL
^ AT PROPORTIONALLIMIT STRESS. PACE GRAIN AT O'OR 90' TO LOAD
3 AVERAGE STRESS IN PLATE AT MAXIMUM LOAD ~ MAM MUM STRESS Or MATERIAL =
^J* AT ULTIMATE STRESS PACE GRAIN AT 0' OR 90' TO LOAD .
C AVERAGE STRESS IN PLATE AT MAXIMUM LOAD  MAXIMUM STRESS OP MATERIAL '
" ' AT ULTIMATE STRESS PACE GRAIN AT 45° TO LOAD
I Z 3 4 5 b 7 8 9
PROPORTIONAL LI MIT 5TRE55 OF MATERIAL t COMPUTED BUCKLING STRESS
Figure 244. — Effectivewidth curves for flat plywood panels in compression.
Ill the use of figure 244, the fiber stress at proportional limit, F cp , is equal to F CPW
when the face grain is parallel to the stiff eners, or F cpx when the face grain is perpen
dicular to the stiffeners. These values may be obtained from table 29 or section 2.600.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
105
When the face grain is 45° to the stiffeners, F ep a may be taken as 0.55 F cu4i , where
F cut $ is determined by section 2.610. The critical buckling stress F, w is determined bi
section 2.701. The procedure for determining effective widths depends upon the range
of stresses under consideration, as follows:
(1) For plywood stresses up to the critical buckling stress, the effective width ratio
(2w/a) may be taken as equal to 1 except when the critical buckling stress is near the
proportional limit of the plywood. This proportional limit may be reached locally when
the average stress is somewhat below the proportionallimit value because of nonuniform
stress distribution across the panel.
(2) Whenever the stress at the edge of the panel (in the plywood adjacent to the
stiffener) exceeds the proportional limit for the plywood, the effective width is determined
from the curves of figure 244, or by interpolating between them, depending upon the
magnitude of the edge stress.
(3) Whenever the stress at the edge of the panel is between the critical buckling
stress of the panel and the stress at proportional limit for the plywood, the effective width
is given by the formula:
2w/a Jl~K)F F +mF dp F c , r ) f2;781
J\r, p " c lT )
where :
/v= value of 2w/a from curve in figure 244 at the ratio F rp /F 0cr .
f = any stress between F, w and F cp .
This formula does not apply when the critical buckling stress is near or above the
stress at proportional limit.
*2.76l Compressive strength. The strength of stiffened flat plywood panels may
be determined by the following method when the stiffeners and their effective widths of
sheet are assumed to act as columns. The effective width of sheet must first be deter
mined as mentioned in section 2.760 after which the following procedure may be used.
The effective modulus of elasticity (£") of the composite section (stiffener plus effective
sheet) is given by the formula:
E , = E b A p +E Le A, t
A.
where :
E b = E w for face grain parallel to stiffeners.
= E X for face grain perpendicular to stiffeners.
For 45° face grain, see section 2.5611.
El c pertains to the species of the stiffener.
i4 P = area of effective panel.
^4 S ( = area of stiffener.
A=A P + A sl .
The effective moment of inertia (/') of the composite section is given by the formula :
r= Y' Ip+ W A " ( xt H) 2+ ir Mi (x ~ v)2 (2:80)
106
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
where :
Ei = E fw for face grain parallel to stiff eners.
= E fx for face grain perpendicular to stiffeners.
For 45° face grain use equation 2:63, section 2.6140.
I r = I of effective panel about its own neutral axis.
= (2w+b)tyi2.
I s t = I of stiffener about its neutral axis.
/= thickness of panel.
d = depth of stiffener.
y = distance from the neutral axis of the stiffener to the stiffener face away from
the panel.
x = distance from the neutral axis of the composite section to the stiffener face away
from the panel.
E b A p {d+)+E Lc A st y }
= E b A p +E^,~A~~t
The internal or calculated averag^stress over the composite section will be P/A,
which should not exceed the allowable stress determined from the following formulas:
Long Columns:
10E'
Fc= (L'uy psi ( 2:82)
where :
L'=L/V~
9 = V~T7~A
(L'/ 9 ) cr = V 15E'/F CU
F
F CU = E' — when the stiffener is critical.
E Lc
F
= E' ~ when the plywood is critical.
■£<&
F cu b = F cuw when face grain is parallel to stiffeners.
=F CU x when face grain is perpendicular to stiffeners.
= F cu q when face grain is at an angle to stiffeners.
When the direction of column bowing is unknown, use the minimum value of F cu
determined for the plywood or the stiffener itself. When the direction of column bowing
is known, the value of F cu for the material on the inside of the curvature may be used.
The value chosen for the fixity coefficient, c, depends on the behavior of the structure
of which the panel is a part, or on the test setup, as the case may be. See section 3.1382
for typical values in structures. In carefully made flatended test panels, a fixity of
c = 3.0 or more is usually developed.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
107
Short columns:
ftR.[i(0]p» (MB)
where:
K = (L'/ 9 ) cr
F cu is same as for long columns when L'/ p approaches (L'/ p) (r . When L'/p is fairly
small, F r „ should be taken as the minimum in the composite section in the longitudinal
direction. This minimum may occur in the plywood or in the stiffener itself.
*2.76l0. Modes of failure in stiffened panels. The procedure in section 2.761 for
short columns assumes that a stiffened panel fails at the instant any longitudinal fiber
of the composite section reaches its crushing stress, based on relative moduli of elas
ticity. Such composite constructions may actually develop an ultimate strength corre
sponding to this assumption, or higher or lower strengths, depending on several factors,
some of which are discussed in the following.
A possible mode of failure, which has been investigated for only one particular type
of construction, is the premature separation of the plywood panel from its stiffeners
occurring when the forces required to restrain the edges of the buckled panels become
too great for the strength of the plywood or its attachment to the stiffeners. (Ref . 210. )
A comparison of the results of this limited investigation with the method of section 2.761,
however, shows the latter to be only slightly unconservative in the worst case. This
comparison also indicates that section 2.761 may be conservative when separation is
F F
prevented and the ratio — — for the stiffeners is higher than — ^ for the plywood.
El c Eb
Since no criteria suitable for general application are available for predicting the
critical modes of failure, it is recommended that typical panels of each particular type
of construction be tested.
A more general investigation of this problem is now under way at the Forest Products
Laboratory.
*2.762. Bending. The maximum bending stress in stiffened plywood panels can be
calculated from the following formula, when the face grain direction is 0° or 90° to the
direction of the span:
A ™£ (2:84)
where :
c' = distance from the neutral axis of the composite section to the extreme longitu
dinal fiber.
El is taken for the species of the outermost longitudinal fiber.
This maximum bending stress should not exceed the modulus of rupture of the ma
terial in which the maximum stress exists. If the stiffener is of an I or box section,
the modulus of rupture must be corrected by a form factor as follows: When the load
is applied so that the outer flange of the stiffener will fail in compression, the proper
form factor to use is that for a beam having the same flange dimensions as the outer flange
of the stiffener, and the same web thickness as the stiffener, but of a depth equal to 2x.
If the load is applied so that the panel will fail in compression, the proper form factor
108
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
STRENGTH OF WOOD AND PLYWOOD ELEMENTS 109
to use is that of a beam having flange dimensions equal to that of the effective sheet
plus the flange of the stiffener adjacent to the panel, and a web thickness equal to that
of the stiffener but a depth of 2{d+t— x). In either case no form factor need be used
if the neutral axis lies within the compression flange.
Formula 2:84 will apply to stiffened panels having the face grain direction 45° to
the length of the stiffener if E', El, and /' are adjusted as indicated for the 45° com
pression case.
2.8 CURVED PLYWOOD PANELS.
**2.80. Buckling in Compression. No information other than the test results on
a few types of plywood construction having the face grain parallel to the length can be
given on the buckling of curved plywood panels in compression. The curves given in
figure 245 represent the averages of the test results obtained on curved panels by the
Hughes Aircraft Company on the plywood constructions noted. The actual const ruc
tions tested were essentially threeply, with the veneers being laminated in the face,
back, and core when the total number of veneers was greater than three. Large positive
deviations from the curves were obtained when the panels did not buckle before the ulti
mate load was reached. For purposes of design, it is recommended that the values from
the curves of figure 245 be divided by 1.15.
Other tests indicate that when the width of a curved panel is greater than 30° of
arc, the buckling stress is approximately the same as that of a complete cylinder of the
same construction and radius of curvature, and may be computed as indicated in sec
tion 2.820.
*2.81. Strength in Compression or Shear; or Combined Compression (or Ten
sion) and Shear. When failure by buckling does not occur, the ultimate strength of
curved plywood panels subjected to compression or shear, or combined compression (or
tension) and shear may be obtained by the method given in section 2.613. This method
is applicable when the face grain direction is at any angle. 
2.82. Circular thinwalled plywood cylinders. (Ref. 2 — 14).
2.820. Compression with face grain parallel or perpendicular to the axis of the
cylinder. The theoretical buckling stress for a long cylinder (to be modified for design
as described later in the section) is given by the formula:
F*r (theoretical) = k E L  (2:85)
where :
El is for the species of the face plies.
t = thickness of plywood
r = radius of cylinder
k is a buckling constant that is a function of „ and is determined from figure
ifj\\rLi
246. In using figure 246, Ei is the flexural stiffness of the plywood in the direction
parallel to the longitudinal axis of the cylinder. E\ is equal to E fu> when the face grain
is longitudinal and is equal to E fx when the face grain is circumferential. Ei is the flex
ural stiffness of the plywood in the circumferential direction. E^ + Eo is equal to E rw +E fI .
110
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Figure 246. — Theoretical curve for long, thin plywood cylinders in axial compression. The ordinates
represent k in the formula P=k E  where P is the buckling stress. The abscissas represent the ratio
r
E l
 where E\ and Eo are the flexural stiffnesses of the plywood.
Because of the steepness of the curve for k at the extreme right and left portions, it
appears advisable to avoid, when possible, the use of types of plywood for which the ratio
Ei
is small or nearly equal to unity.
E \\E%
For use in design, the theoretical buckling stress must be modified as the propor
tionallimit stress is approached. This is accomplished by the use of figure 247. The
proportionallimit stress used with this chart is the compressive proportional limit for
the plywood in the direction of the cylinder axis and is determined from table 29 or
from section 2.600. F CP = F CPW when the face grain is longitudinal. F cp = F cpx when the
face grain is circumferential. The chart is entered along the abscissa with the ratio
F, ,, r (theoretical) /F cp . The design buckling stress, (F Ccr ), is then obtained by multiplying
the ordinate by F cp .
Tests indicate that an increase in strength may be expected when the ratio of length
to radius is approximately one or less. This effect is being further investigated.
Limited amounts of double curvature have negligible effect on buckling stress.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
111
0.1 02 0.3 0.* OS 06 01 08 09 10 /./ II /.3 M IS IA U
T HEORETICAL BUCKLING STRE.5S ( F c CJ . THEORETICAL)
PROPORTIONAL LIMIT 5TP£5S \ '
Figure 247. — Design curve for long, thinwalled plywood cylinders.
*2.821. Compression with 45° face grain. When the face grain is at an angle of
45° to the cylinder axis, the theoretical buckling stress may be taken as the average of
the theoretical buckling stresses obtained by assuming the face grain direction to be:
(1) Parallel to the cylinder axis, (2) circumferential. In using figure 247, however, to
obtain the design buckling stress, the proportionallimit value (F cp ) should be that for
the plywood at 45° to the face grain. F rpii may be taken as 0.55 F cui; „ where F cui5 is
determined by section 2.610.
2.822. Bending. For bending, the design buckling stress determined as for com
pression may be increased 10 percent.
*2.82 3. Torsion. No data on buckling in torsion, suitable for general application,
are yet available. The shear strength when buckling does not occur may be determined
by section 2.612.
2.824. Combined torsion and bending. When design buckling stresses for pure
torsion and pure bending are available, cases of combined loading can be checked by
the following interaction formula:
(£) +
Where :
f,t = applied torsional shear stress.
fb= applied bending stress.
F slc1 =pure torsion design buckling stress
F 6cr = pure bending design buckling stress
112
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
WIDTH OF WOOD MLMBER IN INCHES
1 2 3 4 5 6 7
4i>8/0
WIDTH OF WOOD MEMBERS IN INCHES
Figure 248. — Bearing strength of bolts in spruce parallel to grain.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
113
WIDTH OF WOOD MEMBER IN INCHES
12 3 4 5 6 7
BOL TS IN SPRUCE . SEE SEC TION 2. 902 FOR
BEARING STRENGTH OR OTHER SPECIES. FOR
!Hj[ 'i) ECCENTRIC LOADING (APPLIED ONLY AT ONE END
jjj] OF BOL T) DIVIDE LOAD FROM CURVES BY 2.
BROKEN CURVES APPLY WHEN ALUMINUM
: ALLOY BUSHINGS ARE USED (5LE SECTION 230$.
i;:;lti!itniHm;t!iHi?i;;p;;;f;;;:i::::n;;;i;;;tfff '••
20
IB
14
10
y
I
4 6 6 10
WIDTH OF WOOD MEMBER IN INCHES
12
14
Figure 249. — Bearing strength of bolts in spruce perpendicular to grain
114
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
2.9. JOINTS.
2.90. Bolted Joints.
2.900. Bearing parallel and perpendicular to grain. In determining the sizes of
solid steel aircraft bolts to be used in wood, the strength of the wood in bearing against
the bolts can be obtained from the solid curves of figures 248 and 249. Broken curves
are for use in determining bearing loads of aluminum bushings used in combination with
steel bolts. (Sec. 2.906.) These curves give the allowable ultimate loads for standard
aircraft bolts bearing in spruce, and applied concentric with the centerline of the member,
that is, with the load divided equally between the two ends of the bolt. The allowable
ultimate eccentric loads, that is, those applied at one end of the bolt only, are onehalf
the loads given by these curves.
The value of bolt bearing stress at proportional limit when bearing perpendicular
to the grain is affected to only a slight extent by the L/D ratio. In general, this value
may be found with sufficient accuracy by dividing the ultimate bearing strength by 1.33
for all L/D ratios (sec. 2.1000).
When the bearing is parallel to the grain, however, the value of bolt bearing stress
at the proportional limit varies considerably with the L/D ratio. The bearing stress at
proportional limit then drops rapidly with an increase in L/D, becoming, at an L/D of 9,
less than 50 percent of the bearing stress at proportional limit at an L/D of 1. The crush
ing stress of softwoods parallel to the grain is equal to 1.25 (1.33 for hardwoods) times
the bearing stress at proportional limit, for L/D ratios from to 1, and increases linearly
to 1.7 times at an L/D of 12. This relation, or the factors by which the ultimate bearing
loads parallel to the grain must be divided to obtain the bolt load at proportional limit,
is given in figure 250.
17 \i Mi¥¥¥Win
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Figure 250. — Variation of the ratio of ultimate bearing strength to bearing strength at proportional
limit with L/D for bolts bearing parallel to grain.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
115
9 liiiijiiiilHi ;[:;:. I::;; ;:::;;
r ;■ :::: ;:!; Uu^ tin.
'4 '2 '4 ' c 4
DIAMETER OF CIRCULAR PLATE IN INCHES
Figure 251. — Bearing strength of steel washers in spruce — perpendicular to grain.
Some designers may prefer to work in terms of bearing stress rather than bearing
load. Figures 252 and 253 show the ratio of ultimate bearing stress to ultimate com
pressive stress for bolts loaded parallel and perpendicular to the grain of the wood. The
curves showing ultimate bearing stress parallel to the grain show two cutoffs, one for a
ratio of ultimate stress to proportional limit stress of 1.5 and the other for a ratio of 1.7.
The bolt load curves of figures 248 and 249 are based on the 1.7 cutoff. It is recom
mended that the 1.5 cutoff curve be used if no fitting factor is used in the analysis of
the bolted connection. If a fitting factor is used, the 1.7 cutoff factor can be used with
safety.
2.901. Bearing at an angle to the grain. When the load on a bolt is applied at an
angle between 0° and 90° to the grain, the allowable load (proportional limit or ultimate)
may be computed from the expression
N= — (2:87)
1 P sin* 6+Q cos 2 6 K }
where :
N = The allowable bolt load at angle 6.
P = The allowable bolt load parallel to the grain.
Q = the allowable bolt load perpendicular to the grain.
6 = the angle between the applied load and the direction of the grain.
Equation 2:87 is solved graphically by the Scholten Nomograph, figure 254.
116
ANC BULLETIN— DESIGN OF W OOD AIRCRAFT STRUCTURES
10
9
06
0.7
Ob
0.5
04
03
0.2
0.1
VARIATION IN RATIO OF ULTIMATE
BEARING 5TRE55 TO ULTIMATE COM
PRESSIVE STRESS PARALLEL TO GRAIN
WITH VARIATION IN ^ RAT 10
\
\
cu~,
r OFI
/
7
CO
T OF
~F AT
F brp
10
12.
BEARING LENGTH r DIAMETER ( RATIo)
Figure 252. — Bolt bearing stresses parallel to grain.
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Figure 253. — Bolt bearing stresses perpendicular to grain.
STRENGTH OF WOOD AND
PLYWOOD ELEMENTS
117
118
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
2.902. Bearing in woods other than spruce. The allowable ultimate loads for
bearing of bolts in some species of wood other than spruce may be determined by
multiplying the loads from figures 248 and 249 by the factors given in table 212.
When the bearing stress curves of figures 252 and 253 are used, these correction factors
need not be applied. (The value of K discussed in section 2.904 is also given in this
table.) These factors have been obtained by the following method which can be used
to obtain factors for species not listed in this table. The factor for loads parallel to the
grain is the ratio of the allowable compressive stress at the proportional limit for the
species to the corresponding allowable for spruce. The proportional limit stresses for
compression parallel to the grain are given in column 11, table 23. For compression
perpendicular to the grain the proper factors can be obtained by using the ratio of the
crushing strengths in column 13, table 23, as these values are proportional to the
proportional limit values.
Table 2V2. — Bearing .strengths of other species as compared to spruce
Parallel
Perpendicular
Species
to grain 1
to grain
Spruce
1 .00
1.00
1.00
Douglasfir (coast tvpe)
1.40
1 .55
1 30
Fir, noble
1.02
1.02
1.11
Hemlock, western
1.18
1 .13
1 .09
Pine, eastern white '.
.96
93
1 .12
Whitecedar, Port Orforrl
1 22
1.23
1.20
Birch
1 .37
1 89
.79
Mahogany
1.22
2 10
1 .06
Maple
1 .40
2.58
.69
Walnut
1.42
2.06
1 .07
Yellowpoplar ■
.94
.96
.88
1 These values for hardwoods apply only at the proportional limit. At the ultimate bearing strength they should be
multiplied by the ratio between the ordinates of the curves for hardwoods and softwoods at the appropriate — ratio in
figure 250. D
 See section 2.904.
2.903. Combined concentric and eccentric loadings; bolt groups. When the de
sign loads on a group of bolts are either all concentric or all eccentric and are all in the
same direction, the allowable loads for the individual bolts may be added directly to
determine the total allowable load for the group. When the design loads are in different
directions (as when the load causes a moment about the centroid of the bolt group) or
when they are partly concentric and partly eccentric, each bolt must be treated separ
ately. The design loads and moments must be distributed to each bolt in proportion to
its resistance and the geometry of the bolt group. This often requires a trial and error
calculation.
2.904. Bolt spacings. The following bolt spacing criteria are based on spruce.
For other species, these spacings should be multiplied by the factor K in table 212 or
by the expression:
K =wk„ < 2:88)
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
119
where :
F cp = allowable stress at proportional limit in compression parallel to the grain.
F su = allowable shearing stress parallel to the grain of the material.
2.9040. Spacing of bolts loaded parallel to the grain.
(1) Spacing parallel to the grain. The minimum distance from the center of any
bolt to the edge of the next bolt in a spruce member subjected to either tension or com
pression is given in figure 255. The minimum distance from the edge of a bolt to the
end of a spruce member subjected to tension is also given by this figure.
The minimum distance from the edge of a bolt to the end of a member subjected
to compression should be bolt diameters.
(2) Spacing perpendicular to the grain. The minimum distance between the edges
of adjacent bolts or between the edge of the member and the edge of the nearest bolt
should be one bolt diameter for all species. However, pending further investigation of
the effects of stress concentration at bolt holes, it is recommended that the stress in the
area remaining to resist tension at the critical section through a bolt hole not exceed
twothirds the modulus of rupture in static bending when crossbanded reinforcing
plates are used; otherwise onehalf the modulus of rupture shall not be exceeded.
(3) When a bolt load is less than the allowable load parallel to the grain, the spacing
may be reduced in the following way: The bolt spacing given in figure 255 can t be
multiplied by the ratio of actual load to allowable load except that the spacing should
be not less than three bolt diameters. The bolt spacing perpendicular to the grain
cannot be reduced below one bolt diameter.
2.9041. Spacing of bolts loaded perpendicular to the grain.
(1) Spacing perpendicular to the grain. The minimum distance from the edge of a
bolt to the edge of the member toward which the bolt pressure is acting should be 3 %
bolt diameters. The margin on the opposite edge and the distance between the edges
of adjacent bolts should be not less than one bolt diameter.
(2) Spacing parallel to the grain. The minimum distance between edges of adjacent
bolts should be three bolt diameters and the distance between the end of the member
and the edge of the nearest bolt should be not less than four bolt diameters.
(3) When a bolt load is less than the allowable load perpendicular to the grain, all bolt
spacings may be multiplied by the ratio of actual load to allowable load except that the
spacing should be not less than one bolt diameter. The distance between the end of the
member and the edge of the nearest bolt, measured parallel to the grain, should be not
less than three bolt diameters, however.
2.9042. Spacing of bolts loaded at an angle to the grain. When bolts are loaded
at some angle to the grain, the load can be resolved into components parallel and
perpendicular to the grain and the spacings thereafter determined in accordance with
paragraphs 2.9040 and 2.9041.
2.9043. General notes on bolt spacing. When bushings are used in combina
tion with bolts, the spacing should be based upon the outside diameter of the bushing.
When adjacent bolts or bushings are of different diameters, the spacing should be based
upon the larger.
When staggered rows of bolts are employed in design, the minimum distance between
the center lines of adjacent bolt rows should be not less than the sum of the diameters
of the largest bolt in each row.
120
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
O / 2 J 4 s 6 7 8 9 /O // /2 /3 14
t FWC/</V£5S OF WOOD M£MS£f? /MCHES
Figure 255. — Allowable distances between bolts and allowable end margin for bolts in spruce.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
121
2.905. Effects of reinforcing plates. The allowable concentric bearing load
parallel to the grain for a bolt in a wood member symmetrically reinforced with bearing
plates may be determined as follows :
(1) Compute the L/D ratio based upon the total length of the bolt in bearing.
(2) From figure 252 read the ordinate corresponding to the L/D ratio found in
step (1).
(3) Multiply the factor determined in step (2) by the appropriate maximum crush
ing strengths to obtain the allowable bearing stresses of the materials involved.
(4) Multiply the stresses so obtained by the corresponding bearing areas to obtain
the allowable bearing loads for each material.
(5) The summation of these bearing loads is the allowable bearing load of the rein
forced member.
The preceding method applies to plywood reinforcing plates regardless of the angle
between the load and the face grain direction.
The allowable concentric bearing load perpendicular to the grain can be obtained
in a similar manner except that in step (2) figure 253 shall be used.
When the load on a bolt is applied at an angle between 0° and 90° to the grain the
allowable load may be computed by substituting in equation (2:87) the parallel and
perpendicular bearing allowables determined by the methods outlined in the preceding
paragraphs.
The allowable eccentric bearing load will be onehalf that obtained by the procedures
outlined in preceding paragraphs except that in determining the concentric load, an
allowable bearing stress higher than that of the member may be used only for the plate
on the side on which the load is applied.
Care must be taken that the glued area between the plate and the member is suf
ficient to develop the load absorbed by the plate from the bolt.
In order to prevent splitting at the ends and edges of wood members, and also to
prevent local crushing effects, it is recommended that crossbanded reinforcing plates be
glued under all fittings. Cross bolts may be used to minimize splitting.
2.906. Bushings. Bushings of light alloys or fiber materials may be used to
increase the bearing strength of bolts. Since the possible combinations of materials for
bolts and bushings are numerous, a specific set of allowable loads for all possible combina
tions cannot be given here.
Allowable bearing loads for aluminum bushings used in combination with steel bolts
are given by the broken curves of figures 248 and 249 for a limited number of bushing
sizes. The diameters shown on the curves represent the outside diameters of the bushings.
The allowable bearing loads for other sizes of aluminum bushings used in combination
with steel bolts, and for other combinations of materials, should be determined by a
special test or by a conservative method of interpolation with due consideration of the
materials used.
2.907. Hollow bolts. The use of hollow bolts with comparatively thin walls for
bearing in wood is not recommended, as tests at the Forest Products Laboratory show
that such bolts are little if any more efficient on a weight basis than solid bolts. When
used, the allowable stress parallel to the grain may be obtained from N.A.C.A. Technical
Note 296. (Ref. 228.) In general, tests should be made to determine the allowable
loads at other angles to the grain.
122
ANC BULLETIN— DESIGN" OF WOOD AIRCRAFT STRUCTURES
2.908 Bearing in plywood. For plywood constructed in accordance with specifi
cation ANNNP5111) (Plywood and Veneer, Aircraft Flat Panel) or any other approxi
mately balanced construction (nearly equal thickness of material in both directions)
the ultimate bearing strength of bolts loaded at any angle to the face grain corresponds
very closely to the product of F cuw (ultimate compressive strength parallel to the face
grain), the projected bolt area, and the L/D correction factor shown in figure 252. For
appreciably unbalanced plywood constructions, use F cuw and F cux for bolts loaded at
0° and 90° to the face grain, respectively. For loadings at other angles, use a straight
line interpolation. The most common use in which plywood will have to sustain bolt
bearing loads will be as reinforcing plates on solid wood members (section 2.905).
2.91. Glued Joints.
2.910. Allowable stress for glued joints.
(1) An allowable glue stress equal to onethird F su (column 14 of table 23) for the
weaker species in the joint should be used for all plywoodtoplywood or plywoodto
solidwood joints regardless of face grain direction and for joints between solid wood
members in which the relative grain direction is essentially perpendicular. The reduction
for joints in which the face grain direction of the plywood is parallel to the grain of the
solid wood is necessary primarily because of the unequal stress distribution common
to most plywood glue joints.
(2) The allowable shear stress on the glue area for all joints between pieces of solid
wood having parallelgrain gluing, is equal to the allowable shear stress parallel to the
grain for the weaker species in the joint. This value is found in column 14 of table 23
and should be used only when uniform stress distribution in the glue joint is assured.
2.911 Laminated and spliced spars and spar flanges. Requirements for lami
nated and spliced spars and spar flanges are presented in ANC19, Wood Aircraft In
spection and Fabrication. (Ref. 24. ) Provisions for limiting the location of scarf joints
and for the required slope of grain are included.
2.912. Glue stress between web and flange. The stress on the glue area be
tween web and flange may be determined by dividing the maximum shear per inch in
plywood by the area of contact per inch. For example, the shear stress on the area of
contact is
f e = f ~=l (2:89)
where :
/ fl = shear stress on the area of contact.
/ 5 = the maximum shear stress in the plywood.
/ = thickness of one web.
d = depth of the flange.
q = shear per inch in the plywood.
The allowable stress is determined according to section 2.910. If, for example, the
flange were of spruce and the web were of mahoganyyellowpoplar, the allowable stress
would be onethird the value for spruce, or 283 pounds per square inch.
2.92. Properties of Modified Wood. It is at times desirable to impart modified
properties to wood for reinforcement at joints, bearing plates, and for other specific uses.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
123
Such modifications can be obtained by treating with synthetic resins, by compressing,
or by a combination of treating and compressing.
Investigations at the Forest Products Laboratory have produced several types of
modified wood combinations, such as " impreg," " compreg," "semicompreg," and " stay
pak," which are described in ANC Bulletin 19. When the resin is set within the structure
by the application of heat prior to the application of assembly pressures, thus greatly
limiting the compression of the wood, the material is called "impreg." When the treated
wood is subjected to pressures in the range of 1,000 to 3,000 pounds per square inch
prior to the setting of the resin, resulting in a product with a specific gravity of 1.2 to
1.4, the material is called "compreg." Resintreated wood with specific gravity values
between that of impreg and compreg is known as "semicompreg." Ordinary laminated
wood or solid wood with no resin within the intimate structure when compressed under
conditions that cause some flow of lignin is known as "staypak." It differs from material
made according to conventional pressing methods in that the tendency to recover its
original dimensions when exposed to swelling conditions has been practically eliminated.
Some properties of parallellaminated and crosslaminated modified wood made by
the Forest Products Laboratory from 17 plies of J i6inch rotarycut yellow birch veneer
are presented in tables 213 and 214, respectively. Average values resulting from the
specified number of tests, together with maximum and minimum values, are given.
Values for normal laminated wood (controls), impreg, semicompreg, compreg, and stay
pak are presented. Conclusions drawn from these comparative tests must be regarded
only as indicative, because the number of tests is limited.
2.920. Detailed Test Data for Tables 213 and 214. Specimens for test were ob
tained from three sets of 24 by 24inch panels, each made of 17 plies of X$w.ch yellow
birch veneer. Each set consisted of two panels of each of the five materials, one panel
parallellaminated and one crosslaminated. Panels of a set were formed by assembling
corresponding plies of the panels from successive sheets of veneer as it came from the
lathe. So far as possible, the veneer for each set was taken from a different log or bolt.
Except as otherwise noted, tests were made on specimens with the original or formed
surfaces of the material undisturbed. In general, an equal number of specimens was
tested from each of the two principal grain directions, lengthwise and crosswise (0° and
90°), namely, parallel and perpendicular, respectively, to the grain of parallellaminated
panels, and to the face grain of the crosslaminated panels.
Tension parallel to grain (A, tables 213 and 214). Specimens were 1 inch wide
by panel thickness (t) by 24 inches long, shaped to have a 2 1 2inch long central section
yi inch wide. The taper followed a 90inch radius on each edge.
Tension perpendicular to grain and parallel to laminations (B, tables 213 and
214). Specimens were 1 inch by (t) by 16 inches long, shaped to have a 2 1 "2inch long
central section J 2 inch wide for table 213 and 3^t inch wide for table 214, with radii
of 30 and 60 inches, respectively.
Compression parallel to grain (C, tables 213 and 214) and perpendicular to grain
and parallel to laminations (D, tables 213 and 214). Specimens were 1 inch by (t)
by 33^ to 4 inches long for the controls; impreg and semicompreg specimen lengths were
approximately 4t. Compreg specimens were 1 inch by (t) by 1 inch long for maximum
and proportional limit stresses, and 1 by (t) by 3^2 inches long for modulusoi'elasticity
STRENGTH OK WOOD AND PLYWOOD ELEMENTS
125
Si 1
302.9
14.37
4.8
22 =
3,990
6,130
367.4
183 9
11.60
3.9
4,810
6,370
385.2
*M8 4
12.72
4.33
33.7
4.3
29.4
: ^ ^ c. c.
5,010
8,270
358.8
173.1
6.74
1.30
1
3,160
6,780
315.5
136.8
4.0
.64
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4,070
7,370
333.4
161.2
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126
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
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STRENGTH OF WOOD AND PLYWOOD ELEMENTS
128
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
determinations. Staypak specimens were 1 inch by (t) by 2 and 4 inches long for pro
portional limit and modulus data, and 1 by (t) by 1 and 2 inches long for maximum stress.
Compression perpendicular to laminations (E, tables 213 and 214). Specimens
were 1 by 1 inch by panel thickness (t), except for compreg and staypak, which con
sisted of two thicknesses of material, each 1 inch square, placed one upon the other.
Deformations were measured between the fixed and movable heads of the testing
machine.
Static bending (F and G, tables 213 and 214). Specimens 1 inch wide by height
(t) were tested as a simple beam with center loading on spans ranging from 14t to 16t.
Shear parallel to grain and perpendicular to laminations (H, table 213). Notched
specimens were 2 inches by (t) by 2 1 i inches (as illustrated in figure 13 of A.S.T.M.
specifications for tests of small clear timber specimens, Designation D14327) with
shearing surface 2 inches by (t). Specimens tested in the Johnsontype shear tool were
1 inch by (t) by 3 inches (two 1inch by (t) shearing surfaces).
Modulus of rigidity tests (I, table 213 and H, table 214) were conducted on
panels approximately 24 inches square by full thickness of the material, using the plate
shear method developed by the Forest Products Laboratory for measuring the shearing
moduli of wood, as described in Mimeograph No. 1301.
Torsion tests (J, table 213 and I, table 214) were conducted on rectangular speci
mens of width 3t by thickness (t) by 16 to 24 inches long, gripped flatwise and with
detrusion measuring device applied to their edges. Following tests on these, with
torque kept within the proportional limit, specimens were cut to a width of 2t and the
test repeated.
Toughness (K, table 213 and J, table 214) specimens 5 % by (t) by 10 inches long
with grain of parallellaminated material and face grain of crosslaminated material
parallel to length were tested over an 8inch span on the Forest Products Laboratory
toughness machine with plane of laminations parallel to direction of load.
Impact (Izod type) specimens (L, table 213) had the grain lengthwise and the
notch in an original surface. Some of the staypak specimens were less than inch
thick, but the dimension from the base of the notch to the opposite face was standard.
Water absorption (M, table 213) specimens were 1 by ? 8 by 3 inches. The grain was
parallel to the 1inch dimension. One face was an original surface sanded and the other
surfaces were machined. Specimens were heated for 24 hours at 122° F., cooled, weighed,
immersed in water at room temperature for 24 hours, and the percentage increase in
weight during immersion calculated.
Fabricated thickness changes (N, table 213). Equilibrium swelling and recovery
from compression were determined from specimens }i inch by (t) by 2 inches long (grain
parallel to the J sinch dimension). Specimens were immersed in water at room tem
perature until equilibrium moisture content was reached, and the percentage increase
in thickness (swelling plus recovery) calculated. The specimens were then ovendried,
measured, and percentage recovery and equilibrium swelling determined.
STRENGTH OF WOOD AND PLYWOOD ELEMENTS
129
REFERENCE FOR CHAPTER 2
(21) Elmendorf, A.
1920. . data on the design op plywood for aircraft. N. A.C.A. Tech. Report 84. (Also
Forest Products Laboratory Mimeo. 1302.)
(22) Forest Products Laboratory
1940. wood handbook. U. S. Dept. Agr. Unnumbered Publ. (Revised.)
(23)
1941. specific gravitystrength relations for wood. Forest Products Laboratory
Mimeo. 1303.
(24)
1943. wood aircraft inspection and fabrication. AXC19.
(25) Freas, A. D.
1942. methods of computing strength and stiffness of plywood strips in bending
Forest Products Laboratory Mimeo. 1 304.
(26) Jenkin, C. F.
1920. REPORT ON MATERIALS USED IN AIRCRAFT AND AIRCRAFT ENGINES. (Gr. Brit.) Mu
nitions Aircraft Production Department. Aeronautical Research Committee.
(27) Lewis, W. C. and Dawley, E. R,
1943. stiffeners in box beams and details of design. Supplement to: Design of Ply
wood Webs in Box Beams. Forest Products Laboratory Mimeo. 1318A.
1 2—8) Lewis, W. C; Heebink, T. B.; Cottlngham, W. S.; and Dawley, E. R.
1943. buckling in shear webs of box and Ibeams and the effect upon design criteria.
Supplement to: Design of Plywood Webs in Box Beams. Forest Products Laboratory
Mimeo. 1318 B.
(29) Liska, J. A.
1942. TENTATIVE METHOD OF CALCULATING THE STRENGTH AND MODULUS OF ELASTICITY OF
plywood in compression. Forest Products Laboratory Mimeo. 1315.
(210) Lundquist, E. E.; Kotanchik, J. N.; and Zender, G. W.
1942. a study of the compressive strength of stiffened plywood panels. N. A.C.A.
Advanced Tech. Note. (Restricted.)
(211) March, H. W.
1 941 . SUMMARY OF FORMULAS FOR FLAT PLATES OF PLYWOOD UNDER UNIFORM OR CONCEN
TRATED LOADS. Forest Products Laboratory Mimeo. 1300. (Revised. >
(212)
1942. BUCKLING OF FLAT PLY WOOD PLATES IN COMPRESSION, SHEAR, OR COMBINED COMPRES
SION and shear. Forest Products Laboratory Mimeo. 1316.
(213)
1942. flat plates of ply wood under uniform or concentrated loads. Forest Prod
ucts Laboratory Mimeo. 1312.
(214)
1943. buckling of long, thin plywood cylinders in axial compression. Forest Prod
ucts Laboratory Mimeo. 1322 and supplements 1322A and 1322B.
(215) Markwardt, L. J.
1930. aircraft woods: their properties, selection, and characteristics. N. A.C.A.
Tech. Report 354. (Also Forest Products Laboratory Mimeo. R1079.)
(216)
1938. FORM FACTORS AND METHODS OF CALCULATING THE STRENGTH OF WOODEN BEAMS.
Forest Products Laboratory Mimeo. R1184.
130
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(217) Markwardt, L. J., and Wilson, T. R. C.
1935. STRENGTH AND RELATED PROPERTIES OF WOODS GROWN IN THE UNITED STATES. U. S.
Dept. Agr. Tech. Bull. 479.
(218) Xewlin, J. A.
1939. bearing strength of wood at an angle to the grain. Engineering News Record,
May 11, 1939.
(219)
1940. formulas for columns with side loads and eccentricity. Building Standards
Monthly, December, 1940.
(220) Newlin, .1. A., and Gahagan, J. M.
1930. tests of large timber columns and presentation of the forest products lab
oratory column formula. U. S. Dept. Agr. Tech. Bull. 167.
(221) Newlin, J. A., and Trayer, G. W.
1923. form factors of beams subjected to transverse loading only. N.A.C.A. Tech.
Report 181. (Also Forest Products Laboratory Mimeo. 1310.)
(222)
1924. stresses in wood members subjected to combined column and beam action.
N.A.C.A. Tech. Report 188. (Also Forest Products Laboratory Mimeo. 1311.)
(223)
1930. the design of airplane wing ribs. N.A.C.A. Tech. Report 345. (Also Forest
Products Laboratory Mimeo. 1307.)
(224) Norris, C. B.
1937. the technique of plywood. Hardwood Record, October 1937 to March 1938.
(225)
1943. the application of mohr's stress and strain circles to wood and plywood.
Forest Products Laboratory Mimeo. 1317.
(226) Norris, C. B. and McKinnon, P. F.
1943. compression tests. Supplement to: Compression, Tension, and Shear Tests on
Yellowpoplar Plywood Panels of Sizes that do not Buckle with Tests made at Various
Angles to the Face Grain. Forest Products Laboratory Mimeo. 1328 A.
(227) Norris, C. B. and Voss, A. W.
1943. effective width of thin plywood plates in compression with face grain at 0°
and 90° to load. Forest Products Laboratory Mimeo. 1316 E.
(228) Trayer, G. W.
1925. bearing strength of wood under steel aircraft bolts and washers and other
factors influencing fitting design. N.A.C.A. Tech. Note 296.
(229)
1930. wood in aircraft construction. National Lumber Manufacturers Association.
(230)
1930. the design of plywood webs for airplane wing beams. N.A.C.A. Tech Bull. 344.
(231)
1932. the bearing strength of wood under bolts. U. S. Dept. Agr. Tech. Bull. 332.
(232) Trayer, G. W., and March, H. W.
1931. ELASTIC instability of members having sections common in aircraft construc
tion. N.A.C.A. Tech. Report 382.
(233) Wilsox, T. R, C.
1932. strengthmoisture relations for wood. U. S. Dept. Agr. Tech. Bull. 282.
METHODS OF STRUCTURAL ANALYSIS
131
CHAPTER 3. METHODS OF STRUCTURAL ANALYSIS
TABLE OF CONTENTS
3.0 GENERAL 133
3.00 Purpose 133
3.01 Special Considerations in Static Test
ing of Structures 133
3.010 Element Tests 133
3.01 1 Complete Structures 134
3.01 10 Design Allowances for Test Condi
tions 134
3.01 1 1 Test Procedure 135
3.1 WINGS 135
3.10 General 135
3.11 Twospar Wings with Independent
Spars 135
3.110 Spar Loadings 135
3.111 Chord Loading 138
3.112 Lifttruss Analysis 140
3.1120 General 140
3.1121 Lift Struts " 140
3.1122 Jury Struts 143
3.1123 Nonparallel Wires 143
3.1124 Biplane Lift Trusses . . .' 143
3.1125 Rigging Loads 144
3.113 Dragtruss Analysis 144
3.1130 Single Dragtruss Systems 144
3.1131 Double Dragtruss Systems 145
3. 1 1 32 Fixity of Drag Struts 1 45
3.1133 Plywood Dragtruss Systems. . . .145
3.1 14 Spar Shears and Moments 145
3.1140 Beamcolumn effects (Secondary
bending) 148
3.1141 Effects of Varying Axial Load and
Moment of Inertia 148
3.115 Internal and Allowable Stresses for
Spars 148
3.1150 General 148
3.1151 Wood Spars 149
3.116 Special Problems in the Analysis of
Twospar Wings 150
3.1 160 Lateral Buckling of Spars 150
3.1161 Ribs 150
3.1 162 Fabric Attachment 151
3.12 Twospar Plywood Covered Wings . 151
3.120 Single Covering 151
3.121 Box Type 151
3.13 Reinforced Shell Wings 151
3.130 General 151
3.131 Computation of Loading Curves. 153
3.1310 Loading Axis 153
3.131 1 Loading Formulas 153
3. 1 32 Computation < >f Shear, Bending Mo
ment, and Torsion 155
3.133 Computation of Bending Stresses . 156
3.1330 Section Properties 157
3.1331 Bending Stress Formulas 161
3.134 Secondary Stresses in Bending Ele
ments 163
3.135 Computation of Shear Flows and
Stresses 164
3.1350 General 164
3.1351 Shear Flow Absorbed by Bending
Elements 164
3.1352 Shear Correction for Beam Taper 167
3.1353 Simple D Spar 167
3.1354 Rational Shear Distribution 169
3.13540 Single Cell— General Method. . . 169
3.13541 Two Cell— General Method 171
3.13542 TwoCell FourFlange Wing . . . 176
3.13543 Shear Centers 179
3.136 Ribs and Bulkheads 180
3.1360 Normal Ribs 180
3.13600 RibCrushing Loads 181
3.1361 Bulkhead Ribs 181
3.137 Miscellaneous Structural Problems 182
3.1370 Additional Bending and Shear
Stresses due to Torsion 182
3.1371 General Instability 182
3. 138 Strength Determination 182
3.1380 Buckling in Skin 183
3.1381 Compression Elements 183
3.1382 Stiffened Panels 183
3.1383 Tension Elements 185
3.1384 Shear Elements 185
3.2 FIXED TAIL SURFACES 185
3.3 MOVABLE CONTROL SURFACES . .185
3.4 FUSELAGES 186
3.40 General 186
3.41 Fourlongeron Type 187
3.42 Reinforcedshell Type 191
3.421 Stressedskin Fuselages 191
3.422 Computation of Bending Stresses . 191
3.423 Computation of Shearing Stresses 193
3.43 Pureshell Type 194
3.431 Monocoque shell Fuselages 194
3.44 Miscellaneous Fuselage Analysis
Problems 195
3.441 Analysis of Seams 196
3.442 Analysis of Frames and Rings . . . .196
3.4421 Main Frames 196
3.4422 Intermediate Frames 198
3.443 Effects of CutOuts 198
132
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
3.444 Secondary Structures Within the
Fuselage 198
3.45 Strength Determination 198
3.5 HULLS AND FLOATS 199
3.51 Main Longitudinal Girder 199
3.52 Bottom Plating 199
3.53 Bottom Stringers 200
3.54 Frames. 201
3.55 Strength Determination 201
3.6 MISCELLANEOUS 201
References 203
METHODS OF STRUCTURAL ANALYSIS
3.0. GENERAL.
3.00. Purpose. It is the purpose of the Methods of Structural Analysis portion
of this bulletin to present acceptable procedures for use in determining the internal
stresses resulting from the application of known external loads to wood and plywood
aircraft structures. The basic design procedures that have been developed for use in
analyzing metal structures are generally applicable to the problem of wood structures
provided that suitable modifications are made to account for the differences in physical
characteristics. The designer's attention is directed to existing text material covering
the treatment of common stressanalysis problems not treated herein, and to the current
preparation of an ArmyNavyCivil Bulletin, ANC4 "Methods of Structural Analysis."
It is to be emphasized that the analysis procedures described in this bulletin arc
not presented as required procedures but represent suggested methods that are accept
able to the Army, Navy, and Civil Aeronautics Administration. The nature, magnitude,
and distribution of the loads for which the airplane structure shall be designed are
defined by the applicable specification, regulation, handbook, or bulletin of the procur
ing or certificating agency.
Submission of a stress analysis, although such an analysis employs a method of
procedure which is considered acceptable by the procuring or certificating agency, does
not necessarily constitute satisfactory proof of adequate strength. The stress analysis
should be supplemented by pertinent test data. Unless a structure conforms closely
to a previously constructed type, the strength of which has been determined by test, a
stress analysis is not considered as a sufficiently accurate and certain means of determin
ing its strength. Most desirable is a test of the complete structure under the critical
designloads. However, tests of certain component parts and of specimens employing
generally typical construction and detail design features are of great assistance both in
justifying allowable stresses and in proving analysis methods. In each individual case,
the extent and nature of the structural test program required to substantiate the stress
analysis is specified by the procuring or certificating agency.
3.01. Special Considerations in Static Testing of Structures. Since the allow
able stress values given in Chapter 2, table 23, are based on a definite moisture content
and method of load application, consideration should be given to these variables, both
in using element tests to establish design allowable stresses and in designing structures
to be statically tested as complete structures. Elements include simple structural
members and details, such as panels, stiffened panels, or sections of spars. Complete
structures include wing panels, center sections, fuselage, stabilizer, or other parts in
dividually or in combination. These two types of test will be discussed separately
since they are treated differently.
3.010. Element Tests. A comparison of the design values listed in table 23
with the results of standard tests at 12 percent moisture content (ref. 217) shows
that test results may be made approximately comparable to the design values by the
133
134
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
following methods. Enough tests should be made to cover variability but the required
number will be governed by various factors as discussed in the following.
Case A. When the type of element and the mode of failure are such that the results
of element tests can be directly related to the physical properties of coupons cut from
the materials used in the elements, the results of element tests may be corrected by
the ratio of the design values in table 23 to the test coupon values. Care should be
taken that the elements and the coupons are tested at a slow rate, at the same moisture
content, and under approximately the same timeloading conditions. The test ele
ment should be made of matched materials; for example all stiffeners in a stiffened
panel should be made from the same stock.
Case B. When it is not practicable to correct element tests by means of related
tests on coupons, the following procedure may be employed:
(1) A sufficient number of tests should be made to establish a reasonably reliable
average considering the variability of the materials. Fewer tests will be required and
the scatter of related tests will be reduced if the test results are corrected to the average
specific gravity values listed in table 23 by the methods of section 2.01. For the same
reason, it is desirable to use material of approximately average specific gravity in test
specimens.
(2) The strength should be adjusted to 12 percent moisture by factors from table
22 appropriate to the primary mode of failure. Should failure occur in glued or bolted
fastenings, however, no upward adjustments should be made. It should be recognized
that moisture adjustments are subject to error and should, therefore, be avoided when
ever possible by conditioning test specimens to approximately 12 percent moisture
content.
(3) In element tests it will usually be possible to arrange the test procedure so
that errors due to rate and duration of load will be negligible in comparison with other
experimental errors, for example:
(a) If the maximum load is supported for 15 seconds or more, such as in tests
where the load is added by weight increments, corrections for rate and duration of
load are unnecessary.
(b) If the speciment is loaded at a rate of strain such that the time from zero
load to failure is more than 2 minutes when the testing machine is operated contin
uously, corrections are unnecessary. Thus, if the first stopping point is 25 percent of
the expected ultimate load and the machine takes Yi minute to reach this load, the
rate of strain is sufficiently low.
The time to failure after passing the limit load should be not more than 5 minutes
if possible (slower loading results in lower ultimate loads) since upward corrections
of test values, because of long duration, are considered inadvisable.
(4) After correction of the average test results for moisture, a correction factor
to allow for variability should be applied as follows:
(a) 0.94 when the failure is principally the result of compression, tension, or
bending stresses, or shear in 45° plywood.
(b) 0.80 when the failure is principally due to shear stresses parallel to the
grain.
3.011. Complete Structures.
3.0110. Design Allowances for Test Conditions. When a complete structure
METHODS OF STRUCTURAL ANALYSIS
135
is static tested, it is not usually possible to make the test under the conditions on which
the design values of table 23 are based. Therefore, if the purpose of the test is to prove
the strength of the entire structure at a specified ultimate load regardless of test con
ditions (which is usually the case in order to prove joints and fittings) it is recommended
that the designer investigate the effects of probable test conditions prior to designing
the structure on the basis of table 23.
If it appears that the probable test conditions will cause the strength in the test
to be less than that corresponding to design values in table 23, suitable margins of
safety should be incorporated during the design.
3.0111. Test Procedure. In complex composite structures the effects of moisture
content on overall strength are uncertain. Changes in wood strength may be offset
by stress concentration effects. It is, therefore, desirable that complete structures be
conditioned as closely as possible to 12 percent moisture content at the time of testing.
To minimize effects of rate and duration of load, the time to failure after passing
limit load should be less than 15 minutes if possible.
The ultimate load should be sustained without failure for at least 15 seconds, in
order to insure the test being comparable to design values in regard to time effects.
The above procedure may be varied depending upon the purpose of the test. Agree
ment should be reached with the procuring or certificating agency regarding the test
procedures and methods of correction, if any, prior to conducting major tests.
3.1. WINGS.
3.10. General. Because of the basic differences in their structural behavior,
separate stress analysis procedures are outlined for the following general types of wing
structures :
(a) Twospar wings with independent spars.
(b) Reinforced shell wings.
3.11. TwoSpar Wings with Independent Spars. The methods of analysis pre
sented under this heading are based on the assumption that the spars deflect inde
pendently in bending. Such methods are particularly applicable to twospar fabric
covered wings with drag bracing in a single plane. They may also be applied to two
spar wings having drag bracing in two planes. In such cases, the effect of the torsional
rigidity resulting from the double drag bracing, tending to equalize the deflections of
the two spars, is usually neglected but may be taken into account by the methods of
reference 37.
3.110. Spar loadings. The following method of determining the running loads
on the spars has been developed to simplify the calculations required and to provide
for certain features which cannot be accounted for in a less general method. It is
equivalent to assuming that the resultant air and inertia loads at each section are divided
between the spars as though the ribs were simple beams and the spars furnished the
reactions. Frequently, certain items are constant over the span; then the computations
are considerably simplified.
The net running load on each spar, in pounds per inch run, can be obtained from
the following equations :
(3:1)
136
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Vr= \{C N (af)  C Ma } q+>he iH)
C
1446
(3:2)
where :
y/ = net running load on front spar, in pounds per inch
y r = net running load on rear spar, in pounds per inch
a > °> /> 3> an d T are shown in figure 31 and are all expressed as fractions of the chord
at the station in question. The value of a must agree with the value on which C M a
is based.
q = dynamic pressure for the condition being investigated.
Cm and C u a are the airfoil normal force and moment coefficients, respectively, at
the section in question.
C is the wing chord, in inches.
e is the average unit weight of the wing, in pounds per square foot, over the chord
at the station in question. It should be computed or estimated for each area included
between the wing stations investigated, unless the unit wing weight is substantially
constant, in which case a constant value may be assumed. By properly correlating the
values of e and j, the effects of local weights, such as fuel tanks and nacelles, can be
directly accounted for.
n 2 is the net limitload factor representing the inertia effect of the whole airplane
acting at the center of gravity. The inertia load always acts in a direction opposite
to the net air load. For positively accelerated conditions n% will always be negative, and
vice versa. Its value and sign are obtained in the balancing of the airplane.
Figure 3—1. — Unit section of a conventional 2spar wing. All vectors are shown in positive sense.
If it is desired to compute the airloading and inertia loadings separately, formulas
(3:1) and (3:2) may be modified by omitting terms containing « 2 for the airloading, and
omitting terms containing q for the inertia loading. Then the inertia loading, shear,
and moment curves need be computed for only one condition (say, n 2 = 1.0), the values
for any other condition being obtained by multiplying by the proper load factor.
METHODS OF STRUCTURAL ANALYSIS
137
The computations required in using the preceding method are outlined in tables
31 and 32, in a form which is convenient for making calculations and for checking.
Table 31. — Computation of net unit loadings (constants)
Stations Along Span
1
Distance from root, inches
2
C'/l44  (chord in inches) /144
S
f , fraction of chord
4
j. n ti M
5
b  r  f <3)(D
6
a, fraction of chord (a.c.)
7
i, '
8
e ■ unit wing wt., lbs/sq.ft.*
9
r  a =0®
10
a  f «dMD
11
r  j 0(7)
12
i  f ®(D
15
C/144 b =®/(f)
* Those values will depend on the amount of disposable
load carried in the wing.
The following modifications and notes apply to tables 31 and 32:
(a) When the curvature of the wing tip prevents the spars from extending to the
extreme tip of the wing, the effect of the tip loads on the spar can easily be accounted
for by extending the spars to the extreme span as hypothetical members. In such cases,
the dimension / will become negative, as the leading edge will lie behind the hypothetical
front spar.
(b) The local values of C N , item 14, are determined from the design values of C N
in accordance with the proper spandistribution curve.
(c) Item 15 provides for a variation in the local value of Cm When a design value
of centerofpressure coefficient is specified, the value of Cm should be determined by
the following equation, using item numbers from tables 31 and 32.
C', /o =©[©rP'] (3:3)
(d) When conditions with deflected flaps are investigated, the value of Cm q over
the flap portion should be properly modified. For most conditions, C M<1 will have a
constant value over the span.
138
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Table 32. — Computation of net unit loading* (variables)
CONDITION
q
°»l(»to)
C« or C.P1
at
(Refer also to Table 34)
Cjj^ " (variatior. with span)
Cj^ (variation irtth span)
© * ©
© * ©
© x q
Be X ® x @
@ * ©
y f  (20) x ©) , lbs/lnoh
Distanoe b from root
© x (g)
©  ©
(23) x q
x ® x @
© * @
y  (26) x (lo) , lba/lnoh
C c (variation nrlth span)
© X q
© * ®
y « (3l) x ©» Ib./laoh
(e) The gross running loads on the wing structure can be obtained by assuming
e to be zero; then, items ©, ®, and ® become zero, y f becomes © X®, y r becomes
® X @, and y c becomes ® X ©.
3.111. Chord loading. The net chord loading, in pounds per inch run, can be
determined from the following equation :
[C c q+n x2 fi\ C
Vc=
144
(3:4)
where :
y c = running chord load, in pounds per inch.
C c = airfoil chord force coefficient at each station. The proper sign should be retained
throughout t he computations.
n T 2 = net limit chordload factor approximately representing the inertia effect of the
whole airplane in the chord direction. The value and sign are obtained in the balancing
of the airplane. When C c is negative, n x i will be positive.
140
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
q, e, and C are the same as in section 3.110.
The computations for obtaining the chord load are outlined in table 32, items 28
to 32. The following points should be noted :
(a) The value of C c , item 28, usually can be assumed to be constant over the span.
The only variation required is in the case of partialspan wing flaps or similar devices.
(6) The relative location of the wing spars and drag truss will affect the dragtruss
loading produced by the chord and normal air forces. This can easily be accounted for by
correcting the value of C c . (Sec. 3.1121).
It is often necessary to consider the local loads produced by the propeller thrust
and by the drag of items attached to the wing. The drag of nacelles built into the wing is
usually so small that it safely can be neglected. The drag of independent nacelles and that
of wingtip floats can be computed by using a rational drag coefficient or drag area in
conjunction with the design speed. In general, the effects of nacelles or floats can be com
puted separately and added to the loads obtained in the design conditions.
3.112. Lifttruss analysis.
3.1120. General. In considering a lifttruss system for either a monoplane or
a biplane and, in the subsequent investigation of the dragtruss system, due attention
should be given to all the force components which will be applied to the attachment
points by the lift truss.
3.1121. Lift struts. Consider the strutbraced monoplane wing shown in figure
32. The spars in the figure are shown perpendicular to the basic wing chord (the
reference line for normal and chord loads is the M.A.C. of the wing). If the spars are
not perpendicular to the chord reference line, the resultant of the chord and normal
loads should be resolved into components parallel and normal to the spar, as shown in
figure 33a. Also, in the general case, the drag truss will not be perpendicular to the spar
face. This angularity should be considered (fig. 33b), unless it is of small order, which
would result in a negligible correction.
The vertical reactions on the front and rear spars from the lift struts may be de
termined by taking moments about point C (fig. 32) of all the external loads on the
M, f Mr
spars (sec. 3.114). Then R,= ; and R r = , where M,. f and M rr are the moments
g
about the sparroot attachment, point C, of the front and rear spars, respectively.
The strut and spar axial loads may be determined by graphical or analytical methods
on the basis of the truss A B C, if the fitting is eccentric to the neutral axis of the spar.
If the graphical method is used, the correction for angularity of the strut to the VH
plane should not be overlooked.
The strut loads also can be determined by the following formula, which includes the
correction for angularity:
i M true length ,„ _ N
Strut load =rX ^—rjl #1, v u i ^ 3:5 ^
n projected length in VH plane
After the loads in the struts have been determined, the axial load in each spar is:
(strut load) X (—). and the chord component acting on the wing from each strut is:
D
(strut load ) X (— )
METHODS OF STRUCTURAL ANALYSIS
141
(a) DRAG TRUSS PERPENDICULAR TO SPAR FACE
C'<!
(b) DRAG TRUSS NOT PERPENDICULAR TO SPAR FACE
Figure 33. — Resolution of forces into components acting on spars and drag truss.
142
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
METHODS OF STRUCTURAL ANALYSIS
143
When an eccentricity, e, in the root fitting exists, the chord loads and reactions will
act in a plane which generally is not parallel to the line AC. The effect of the eccentricity
is to modify the vertical reactions at the strut point and root. The increment of reaction
R h e
to be added or subtracted is: AR = —  (fig. 34d). Then, the total vertical reaction
component at the strut point is R + AR. It is, at once, apparent that the value of the
dragtruss reaction, R h , is a function of the strut load (fig. 34c); therefore, if extreme
accuracy is desired, it becomes necessary to solve for the reactions on the lift and drag
truss by means of simultaneous equations which include expressions for all the unknowns
involved. The reactions may also be determined by trial and error with comparable
results if sufficient trials are made. However, unless the value of AR is in excess of 2
percent of R, it is considered satisfactory to assume that the total reaction is R+ AR.
3.1 122. Jury struts. In computing the compressive strength of lift struts which are
braced by a jury strut attached to the wing, it is usually satisfactory to assume that a
pinended joint exists in the lift strut at the point of attachment of the jury strut. The
jury strut itself should be investigated for loads imposed by the deflection of the main
wing structure. An approximate solution based on relative deflections is satisfactory,
if the jury strut is conservatively designed to withstand vibration of the lift strut.
When the jury strut is considered as a point of support in the wingspar analysis, rational
analysis of the entire structure should be made. (ref. 317).
3.1123. Nonparallel wires. When two or more wires are attached to a common
point on the wing, but are not parallel, the distribution of load between the wires may be
determined by least work or equivalent methods. The following approximate equations
may be used for determining the load distribution between wires, provided the loads so
obtained are increased 25 per cent.
B =beam component of load to be carried at the joint.
P { =load in wire 1.
P2 = load in wire 2.
Vi= vertical length component of wire 1.
V 2 = vertical length component of wire 2.
A i and A 2 represent the areas of the respective wires.
Li and L 2 represent the lengths of the respective wires.
The chord components of the air loads and the unbalanced chord components of
the loads in interplane struts and lift wires at their point of attachment to the wing should
then be assumed to be carried entirely by the internal drag truss.
3.1124. Biplane lift trusses. In biplanes that have two complete lifttruss and
dragtruss systems interconnected by an N strut, a twisting moment applied to the wing
cellule will be resisted in an indeterminate manner, as each pair of trusses can supply a
(3:6)
(3:7)
where :
144
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
resisting couple. An exact solution involving the method of least work, or a similar
method, can be used to determine the load distribution (ref. 316). For simplicity,
however, it may be assumed first that all the external normal loads and torsional forces
about the aerodynamic center of the cellule are resisted by the lift trusses. This as
sumption is usually conservative for the lift trusses, but does not adequately cover the
possible loading conditions for the drag trusses. A second condition should therefore be
investigated by assuming that a relatively large portion (approximately 75 percent)
of the torsional forces about the aerodynamic center of the cellule are resisted by the drag
trusses. In the case of a singlolifttruss biplane, the drag trusses must, of course, resist
the entire moment of the air forces with respect to the plane of the lift truss.
3.1125. Rigging loads. Wirebraced structures should be designed for the
rigging loads specified by the procuring or certificating agency. Sometimes it may
be necessary to combine the rigging loads with internal loads from flight or landing
conditions.
The effects of initial rigging loads on the final internal loads are difficult to pre
dict, but, in certain cases, may be serious enough to warrant some investigation. In
this connection, methods based on least work or deflection theory offer the only exact
solution. Approximate methods, however, are satisfactory if based on rational as
sumptions. As an example, if a certain counterwire will not become slack before the
ultimate load is reached, the analysis can be conducted by assuming that the wire is
replaced by a force acting in addition to the external air forces. The residual load from
the counterwire can be assumed to be a certain percentage of the rated load and will,
of course, be less than the initial rigging load.
3.113. Dragtruss analysis.
3.1130. Single dragtruss systems. Single dragtruss systems are employed
in strut or wirebraced wings where the ratio of the span of the overhang to the mean
chord is not excessive. The requirements of the specific agency involved should be
reviewed in regard to the upper limit on this value above which doubledrag bracing
is required.
An example of a conventional drag truss is shown in figure 34 for a strutbraced
monoplane wing. The chord loading, C, in pounds per inch run (fig. 34 (a)) may be
distributed to the panel points of the truss (b) as concentrated loads 1, 2, 3, 4, etc. In
addition to the chord loads due to air load, the lift struts also apply loads in the chord
plane. In section 3.1121, the method of determining the chord components was given.
These components are shown in figure 34 (c), assuming that the wing is so loaded
that the lift struts are subjected to tensile loads. If items of concentrated weight, such
as fuel tanks and landing gear, were not accounted for when the running chord load
was computed in table 32, the resultant inertia loads from these items of weight should
be applied to the drag truss. In figure 34 (d) are shown all the loads and reactions
acting on the drag truss.
The loads in the dragtruss members may now be determined by graphical or
analytical methods. Exact division of the drag reaction, R D , on the truss is generally
indeterminate, insofar as the front and rear rootspar attachments are concerned. In
general, overlapping assumptions should be made, or the drag reaction conservatively
assumed to be resisted entirely by one root fitting. Occasionally, the drag reaction
may be divided equally between the front and rear rootspar fittings if they have ap
METHODS OF STRUCTURAL ANALYSIS
145
proximately the same rigidity in the drag direction.
3.1131. Double dragtruss systems. A double drag truss is employed in canti
lever wings or braced wings where it is necessary to provide additional torsional rigidity
outboard of the strut point. The investigation of doubledrag trusses follows the same
line of procedure outlined in section 3.1130. The design of the double truss is usually
dictated by torsional rigidity requirements rather than by the actual design loads
applied to the structure.
In showing compliance with requirements in which the upper drag wire in one
bay and the lower drag wire in the adjacent bay are assumed in action (the remaining
wires in these two bays assumed to be out of action), the loads on the strut take the
form shown in figure 35. R wu and A',,,; represent the wire force components along the
drag strut. In general, it will be necessary to balance these components in the drag
direction by a reaction, R w i — R wu \ then, taking moments about a convenient point,
the vertical couple force R c may be determined. Having the forces and reactions on
the drag strut, the internal forces readily may be determined.
[ Compon ents Along Drag Strut
"[Emm Wires
V
Se ction A A
Figure 35. — Double drag truss — two drag; wires in action.
3.1132. Fixity of drag struts. Drag struts should be assumed to have an endfixity
coefficient of 1.0, except in cases of unusually rigid restraint, in which a coefficient
of 1.5 may be used.
3.1133. Plywood dragtruss systems. In a twospar, plywoodcovered wing,
the plywood covering, together with the drag struts, is usually depended upon to carry
the chord shear. Section 3.12 gives methods of analysis of this type of structure.
3.114. Spar shears and moments. The fundamental principles of statics should
be employed in the determination of wingspar shears and bending moments. Before
proceeding with the detailed determination of these items, it is essential, in order to
avoid errors, that all the external loads and reactions be determined for the spar.
The primary bending moments at various stations on a cantilever spar may be
146
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
determined conveniently by the equation :
M x =M 1 ±Six£
Fa
(3:8)
where Mi and S x are the moment and shear at station 1 ; x, the distance between station
1 and x; and > Fa, the sum of the moments about station x of all the loads acting
between the stations. It will be found desirable to prepare a table similar to the one
shown in figure 36 to facilitate the computations. If the distances between the var
ious stations are relatively small, the center of gravities, a, of the trapezoidal loadings
f '
1
"1
» n
2 (
n
/
/
d l — »
*a3»
d 2^
d 3 ^
<»!»
d4 ,
1
2
3
4
5
6
7
8
9
10
11
Section
Distance
from
Root
Distance
between
Sections
d
Load
per in.
w
Average
load
per in.
w a
Load
between
Sections
F
Arm to
centroid
(1)*
a
Moment
11' • Fa
Shear
S  £F
Moment
H" • Sd
Moment
at
Section
4
d 4
w 4
d 4  dj
w 4* w 3
2
Item ®
X
Item ()
(1)*
■l
(2)*
F43
x a} "*~
U
3
d 5
w 3
F 4 3
<
d 3 d 2
Wj+Wg
2
Item ©
X
Item (5)
a 2
F32
(3)»
S3 X
(d s d 2 )
2
dg
w 2
F 43+
F 32
d 2 d x
w 2* w l
2
Item (3)
X
Item ©
a 3
F21
x a 3
1
d l
w l
F 43 +
F32 ♦
F21
"0
1
NOTES
(1) The center of gravity of a trapezoidal loading may be determined by the formula x = 2+R
e 3(1*R)
where R ■ h2 ; then a\  x(d 4 dj)
h x
(3) Sj, Sg etc. is shear at stations 3, 2, etc. (Item 9)
T
h 2
;
:
T
1
c
Figure 36. — Determination of shears and bending moments.
METHODS OF STRUCTURAL ANALYSIS
147
(«) BINDING MOMENT and SHEAR DIAORAM  CAHTHEVZR gPAR
STRUT LOAD » v
Figure 37. — (a) Bending moment and shear diagram — cantilever spar, (b) Bending moment and shear
diagram — braced spar.
148
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
may be assumed to lie midway between the stations with negligible error and slightly
conservative results. If concentrated loads exist at points on the span, the table may
be modified easily to account for these loads.
The case of an externally braced spar may be handled in a manner similar to that
for the cantilever spar, insofar as the determination of the shears and moments out
board of the strut and the moment at the root due to external loads are concerned.
The root moment required in section 3.121 to determine the liftstrut reactions may be
obtained conveniently by the foregoing procedure.
The general form of the moment and shear curves is shown in figure 37, (a) and
(6), for braced and cantilever spars. It always is desirable to plot the bending moment
and shear curves as a general check of the computations and to facilitate the investi
gation of stations along the span not covered in figure 36.
3.1140. Beamcolumn effects. (Secondary bending). In connection with the
bending moment and shear curves for a braced spar inboard of the strut point, where the
spar is loaded as a beam and a column simultaneously, the effects of secondary bending
should be taken into account by use of the "precise" equations or the "polar diagram"
method. The solution of the beamcolumn problem is covered extensively in several
textbooks relative to airplane structures, and, therefore, will not be covered here (refs.
31, 315). It is necessary, however, to base such computations on ultimate loads rather
than on limit loads, in order to maintain the required factor of safety. Continuous
spars having three or more supports should be investigated by means of the three
moment equation or other methods leading to equivalent results.
3.1141. Effects of varying axial load and moment of inertia. The dragtruss bays
of a braced wing usually are shorter than the lifttruss bay, as indicated in figure 34.
The axial loads in the spars due to the chord loading, therefore, vary along the span.
Although the "precise" equations for a beamcolumn assume a constant value of axial
load in the beam, it is generally satisfactory to determine a weighted value of axial
load for use in determining the "precise" bending moment . Referring to figure 38:
U _1 J \ Li + Po L2+P3 L3
'  L^U+U < (3:9)
where P c is the weighted axial load due to chord loading, and P h P%, and P 3 are the spar
axial loads in the drag bays 1, 2, and 3. The total axial load in the spar is :
p,=p s + p c (3:10)
where P s is the spar axialload component from the lift strut or wire.
Generally, the moment of inertia, I, also varies along the span and a weighted value
of / may be determined for use in the "precise" equations, as follows:
T _1 1 L\\p2 L2+/3 L3 .
where 1 1, 1 2, and 7 3 are the moments of inertia in bays 1, 2, and 3. If the " polar diagram"
method is used, the actual variation can be taken into account.
3.115. Internal and allowable stresses for spars.
3.1150. General. The allowable stresses for spars may be found in section 2.3.
In beams subjected to combined bending and compression, the margin of safety computed
METHODS OF STRUCTURAL ANALYSIS
149
r
Wlb.per In.
<
< L 2 >
, L 5 >
Figure 38. — Distribution of forces on wood spar section.
by a simple comparison of the internal and allowable stresses may be meaningless,
particularly when the beamcolumn is approaching the critical buckling point. True
margins of safety may, therefore, be determined only by successive approximations.
For example, if a spar is rechecked after increasing all external loads and moments by
10 per cent, and still found satisfactory, the true margin of safety is at least 10 per cent.
3.1151. Wood spars. In general, a spar will be subject to bending, axial (tension
or compression), and shear stresses. The total stress due to bending and axial load may
be computed by the usual expression:
f,=^+ ,3:12,
where M includes secondary bending. In computing the section properties of a wood
spar, the following points are worthy of attention. Consider the spar section shown
in figure 39.
(a) Where the two vertical faces of the spar are of different depths, the average
depth of the section may be used, as shown by h.
(b) If the webs are plywood, only those plies parallel to the spar axis and one
quarter of those plies at 45° may be used in the computation of A and / of the sections.
These are approximate rules to allow for the difference in modulus of elasticity of the ply
wood and the solid wood. If the plywood webs are neglected entirely, the computation
of the section properties is simplified and the results are more conservative.
(c) When investigating a section, such as A— A in figure 39, the full section should
be considered effective only if the glue area is sufficient to develop the full strength of
the side plates. In general, the distance a should not be less than 10 times or 15 times
the thickness of a side plate for softwoods and hardwoods, respectively. The reinforcing
blocks should be beveled, as shown, to prevent stress concentration which may lead to
consequent failure in the glued joint at the edge of the reinforcement.
(d) Filler blocks may likewise be used in computing the section properties, provided
the length of the blocks and their glue area to webs and flanges is sufficient to develop the
required bending stresses.
(e) In the detailed investigation of a spar section, the reduction in strength due to
bolt holes should be considered when computing the section properties. In computing
t
150
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
the area, moment of inertia, etc., of wood spars pierced by bolts, the diameter of the bolt
hole should be assumed greater than the actual diameter by the amount specified by the
procuring or certificating agency. In computing the properties of section AA (fig. 39),
it should be assumed that all the bolt holes pass through the section, because failure
might actually occur along the line uv.
Section AA
SOLID SPAR
Figure 39. — Wood spar section.
The longitudinal shear stress in the web of a spar may be obtained from the ex
pression :
SQ
b'l
(3:13)
In the determination of Q, for spars with plywood webs, the recommendations in (6)
should be followed. However, the value of b' in the expression should be the total web
thickness. For tapered spars, the shear stress may be reduced to allow for the effects
of taper in accordance with section 3.1352.
3.116. Special problems in the analysis of twospar wings.
3.1 160. Lateral buckling of spars. For conventional twospar wings, the strength
of the spars against lateral buckling may be determined by considering the sum of
the axial loads in both spars to be resisted by the spars acting together. The total
allowable column strength of both spars is the sum of the column strengths of each spar
acting as a column the length of a drag bay. Fabric wing covering may be assumed to
increase the fixity coefficient to 1.5. When further stiffened by plywood or metal lead
ingedge covering extending over both surfaces forward of the front spar, the fixity coeffi
cient may be assumed to be 3.0.
3.1 161. Ribs. Analytical investigation of a rib generally is not acceptable as proof
of the structure. In some cases, however, a rib may be substantiated by analysis when
another rib of similar design has been analyzed, and subsequently strengthtested. In
METHODS OF STRUCTURAL ANALYSIS
151
general, it may be desirable to analyze a rib in order to determine the approximate
sizes of the members.
3.1162. Fabric attachment. Although the fabricattaching method usually is not
stress analyzed, it is, of course, important that the riblacing strength and spacing
be such that the load will be adequately transmitted to the ribs. The specifications of the
procurement or certificating agency in regard to lacingcord strength and spacing should
be followed. Unconventional fabricattachment methods should be substantiated by
static tests or equivalent means to the satisfaction of the agency involved.
3.12. Twospar Plywood Covered Wings.
3.120. Single covering. Twospar wings covered with plywood on only one surface
(upper or lower) should be considered as independent spar wings, in accordance with
section 3.11, and the plywood covering designed to carry the chordwise sheer loads with
the ribs functioning as stiffeners and load distribution members. The center of shear
resistance of the plywood covering may be eccentric to the applied drag load (fig. 315 b).
The resulting torque will then be resisted by a couple consisting of upanddown forces
on the two spars.
3.12 1. Box type. Twospar wings with both upper and lower surfaces covered with
plywood, forming a closed box, should be treated as shell wings in accordance with section
3.13.
3.13. Reinforced Shell Wings.
3.130. General. The types of wing structure considered under this heading are
those in which the outside covering or skin, together with any supporting stiffeners,
resists a substantial portion of the wing torsion and some of the bending. Various types
of shell wings may be classified according to: the number of vertical shear webs, or
number of "cells" into which these webs divide the wing section; whether the span wise
material is concentrated mainly at the shear webs or distributed around the periphery
of the section as longitudinal stiffeners; whether the skin is "thin" so that it buckles
appreciably at ultimate load, or "thick" so that it does not buckle appreciably. Typical
shell wing sections are shown in figure 310.
In shell wings the distributed airloads normal to the surface are carried to the ribs
by the skin and its stiffeners. The ribs maintain the shape of the section and transmit
the airloads from the skin to the vertical shear webs or to other portions of the skin
such as the leading edge, which are capable of carrying vertical shear. Main or "bulk
head" ribs perform similar functions for concentrated loads, such as those due to nacelle
landing gear, and fuselage reactions. The vertical shear from the ribs is carried to the
wing reaction points by the shear webs and portions of the skin. The shear in these ele
ments creates axial bending stresses in the beam flange material. When comparatively
stiff spanwise stiffeners are used, they also act as effective flange material, receiving their
axial loads from the webs through shear in the skin. The contribution of the skin to the
bending strength of the wing depends on its degree of buckling and relative modulus of
elasticity.
From this general picture, it is evident that broad simplifying assumptions are
necessary to make a stress analysis of a shell wing practicable, and that the computed
stresses in the various elements are likely to be less exact than in the case of statically
determinate independent spar wings. In metal shell structures, elements which become
too highly stressed generally yield without difficulty and the load is redistributed to less
152
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
SINGLE CELL SECTIONS
MULTICELL SECTION
Note: Other types of Two Cell Wing Sections may have stiffeners.
or thick skin similar to the single cells shown above.
Figure 310. — Typical shell wing sections.
METHODS OF STRUCTURAL ANALYSIS
153
highly stressed elements. In wood structures, however, some types of elements are un
able to accommodate themselves to secondary stresses which would be of no importance
in metal structures, for example, buckles of sharp curvature relative to the thickness
are apt to split plywood. The stress analysis methods presented in this section should
therefore be considered only as reasonable approximations until the designer has had
experience in applying a particular method to a particular type of structure and has
correlated the analysis procedures with the results of static tests.
3.131. Computation of loading curves.
3.1310. Loading axis. In determining the shear and bending stresses in shell
wings, it has been found convenient to transfer the distributed air and inertia loads
to a suitable spanwise loading axis by computing net beam, chord, and torque load
ings at points or stations along such axis. The position of the loading axis may be
chosen arbitrarily if the corresponding moment and torque components acting at a
particular section of the wing are then properly applied to the various elements of the
section in a manner consistent with their structural behavior. Since a reinforced shell
wing is usually a complex nonisotropic structure in which some of the elements resist
axial loads in a particular direction only, the true stress conditions resulting from the
interaction of elements having various directions at a given section are often difficult
to analyze. It is therefore recommended that the loading axis be located inside the
wing, approximately parallel to the principal bending and shear elements. Such a loca
tion should tend to reduce errors in the process of transferring external loads and torques
to the loading axis and redistributing them to the structural elements. Section 3.135
shows that the use of a loading axis in the main shear web is often convenient for the
shear distribution analysis, without further transfer of loads and torques.
If the loading axis is located as suggested, it is necessary for it to change direc
tion where the principal structural elements change direction; for example, where an
outer wing panel having dihedral or sweepback joins a straight center section. The
loadings due to the air and inertia loads are computed for each segment of the axis
in the usual manner, but at the point of direction change, the total moments and torque
from the outboard segment should be resolved into the proper components relative
to the inboard segment.
The formulas given in section 3.1311 for computing the running loads and torque
at various stations on the loading axis use airfoil moment coefficients (or center of
pressure locations) based on airfoil sections parallel to the airflow. For a loading axis
which is not perpendicular to such sections, these equations will therefore give small
errors in the bending moment and torque values. These errors may be neglected unless
the angle of inclination of the loading axis is large.
3.1311. Loading formulas. The net running load at points along the loading
axis and the net running torsion about these points may be found from the following
equations :
C
yb = (C N q + n 2 e) —
(3:14)
(3:15)
154
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
m« = [ \C N (xa) + C_y a } q+n 2 e (xj)J ^ (3:16)
where :
ijb = running beam load in pounds per inch of span.
y c = running chord loads in pounds per inch of span,
m, = running torsion load in inchpounds per inch of span,
a, j, and x are expressed as fractions of the chord at the station in question and locate
points on figure 311 as follows:
a locates the point in the airfoil on which the moment coefficient, CW , is based.
j locates the resultant wing dead weight at the station.
x is the distance from the leading edge to the loading axis, at the station.
q = dynamic pressure for the condition being investigated.
C N and CWo are the airfoil normal and moment coefficients at the section in question.
C c = airfoil chord coefficient at each station. The proper sign should be retained
throughout the computations.
C"=the wing chord, in inches.
e = the average unit weight of the wing, in pounds per square foot, over the chord
at the station in question. It should be computed or estimated for each area included
between the wing stations investigated, unless the unit wing weight is substantially
constant, in which case a constant value may be assumed. By properly correlating the
values of e and j, the effects of local weights, such as fuel tanks and nacelles, can be
accounted for directly.
n2=the net limit load factor representing the inertia effect of the whole airplane
acting at the center of gravity. The inertia load always acts in a direction opposite to
the net air load. For positively accelerated conditions n% will always be. negative, and vice
versa. Its value and sign are obtained in the airplane balancing process.
n r 2 = net limit chordload factor approximately representing the inertia effect of
All Vectors Are Shown in Positive Sense
Figure 311. — Section showing location of load axis.
i
METHODS OF STRUCTURAL ANALYSIS
155
the whole airplane in the chord direction. The value and sign are obtained in the air
plane balancing process. Note that, when C c is negative, 7i x2 will be positive.
Positive directions for all quantities are shown in figure 311. The computations
required for this form of analysis can be carried out conveniently through the use of
tables similar to tables 33 and 3 4.
Table 33. — Computation oj net loadings (constants)
Stations Along Span
1 Distance from root, inches
2 C/144  (chord in inches) /14A
3 x, fraction of chord
4 a, fraction of chord (a.o.)
5 j, fraction of chord*
6 e » unit wing wt. , lbs/ sq.ft.*
7 x  a d).(4)
8 xj(D(D
9 iSlZ
144
* These values will depend on the amount of disposable
load carried in the wing.
The values of yb, y c , and m t should be plotted against the span, and, in case irregu
larities are found, they should be checked before proceeding with the calculations.
It is sometimes desirable to compute the airloadings and inertia loadings separately.
The inertia loading, shear, moment and torsion curves then need be computed for only
one condition (say, rig = 1.0), the values for any other condition being obtained by
multiplying by the proper load factor. The foregoing formulas may be modified for
this purpose by omitting terms containing n 3 for the airloading, and omitting terms
containing q for the inertia loading.
3.132. Computation of shear, bending moment and torsion. The summation of
the areas under the loading curves determined by the method described in section 3.131,
from the tip to any wing station will give the values of the total load (shear) and of
the total torque (torsion) acting at the station.
It is advisable to plot curves of the shear and torsion values against the span to
determine if any irregularities have occurred in the computations. If concentrated
weight and load items were not accounted for in the loading computations, they should
be taken care of by additional computations, and their effects shown on the shear and
torsion curves.
The bending moments at any station of the wing can be found either by computing
the moments, about the station, of the areas under the loading curves outboard of the
station, taking into consideration moments due to concentrated loads, if such are present;
156 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Table 34. — Computation o] net loadings (variables)
COHDITIOH
q
\(etc)
\
Distance b from root
(Refer also to Table 32)
Normal Load
10
U.
12
13
14
C™ (variation with span)
c tfl  © x q
@ * ©
7b  ©x© lba./in.
Chord Load
15
16
17
18
19
c' c (variation with span)
C'fjq  © X q
© ♦ ©
y  ©>© lbs./in.
Unit Torque
20
21
22
23
24
25
26
(variation with span
© x ©
© + (§)
(22) x q
© x ©
@ ♦ @
H  © X©
or by summing up the areas under the shear curves from the tip to the station. A con
venient tabular method of computing these values is also shown in figure 36; and
typical curves are shown in figure 37.
The following quantities are now assumed to have been determined and plotted
for any station on the loading axis:
S bL , the total beam load (shear) through the loading axis in pounds.
S CL , the total chord load (shear through the loading axis in pounds.
M tL , the torsion about the loading axis in inchpounds.
M bL , the beam moment in inchpounds.
M CL , the chord moment in inchpounds.
Formulas of section 3.1311 give moments and torques whose magnitudes and
directions are not necessarily consistent with the direction of the loading axis, but the
errors may usually be neglected. (Sec. 3.1310).
3.133. Computation of bending stresses. The methods outlined herein are based
on the application of the conventional bending theory to the wing section as a whole,
rather than to individual spars deflecting independently. It is assumed that the axial
METHODS OF STRUCTURAL ANALYSIS
157
deformation due to bending, for any element of the wing section, is proportional to
the distance of the element from the neutral axis of the section. This means that in
multispar shell wings the deflection of all spars is assumed to be substantially the same.
These assumptions are valid only where the wing contains relatively rigid torsion cells
so that wing twist is resisted by shear in the walls of these cells rather than differential
bending of the beams. Experience indicates that this simple bending theory is satis
factory for the practical design of shell wings if allowances or corrections are made for
the following conditions:
(1) Excessive shear lag, or shear deflection, in the shell bet wo 311 various bending
elements. Such deflections cause the actual stresses in elements remote from the vertical
shear webs to be less than, and the stresses in elements adjacent to the shear webs
greater than, the values indicated by the simple bending theory. In some types of
structures as described in section 3.1330 (5), these deflections may be considered
negligible in the design of the wing as a whole. Since the bending elements receive and
give up their axial loads through shear in the webs or skin to which they are attached,
local shear stresses and deflections will be intensified in the region of discontinuities in
the bending or shear elements. Shear lag is therefore likely to be appreciable in such
regions. A convenient method of allowing for shear lag is to assume a reduced effective
area for the bending elements affected, in computing the section properties as described
in section 3.1330. The stresses computed for such elements by the bending theory will
then be too high, and, to be consistent, should be reduced in the same ratio as the areas
used in the section properties.
(2) The effects of torsion on the bending stresses at the corners of a box beam.
This condition is usually dealt with after the bending stresses and shear distribution
have been determined on the basis of the simple theory. See section 3. 1370 for discussion.
3.1330. Section properties. A sufficient number of stations along the wing should
be investigated to determine the minimum margins of safety. The information neces
sary to compute the section properties at each station selected for investigation may
be conveniently obtained from a scale diagram of the wing section. Such a diagram
(fig. 312) and accompanying data should show the following:
(1) All material assumed acting in shear or bending (sec. 3.138) divided into
suitable elementary strips and areas, with each such element designated by a suitable
item number for use in tabular computations.
(2) Thicknesses of skin and web elements, area and center of gravity of stiffeners
and flanges, and the relative moduli of elasticity of all elements, normal to the section
(sees. 2.1210, 2.52, and 3.138, or table 29). For example, the modulus of the beam
flanges might be taken as a basic in tension and the moduli of other elements expressed
as ratios thereto.
(3) Reference axes from which the various elements are located. The amount of
calculation will generally be less if the reference axes are made parallel to the beam
and chord directions used in the loading curve determinations.
(4) Effective widths of skin assumed acting in compression in conjunction with
stiffeners or flanges. These should be consistent with the methods used in determining
allowable stresses, in accordance with section 3.138.
(5) Effectiveness factors for bending elements which have elastic modulus different
from the basic value selected for the wing, or which are affected by shear lag. The
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
METHODS OF STRUCTURAL ANALYSIS
159
final factor, c, includes both effects, and may be expressed as: f = f,x«», where e, is equal
E
to * Umcnt an( j e j s f ne s hear lag factor.
TP
Ei basic
A value of Ci = 1.0 indicates that the effectiveness of an element is not considered
reduced by shear lag, while e 2 =0 indicates that it is completely ineffective. Shear lag
may be general or local or a combination of both. General shear lag is greatest in a shell
wing which has a major portion of the bending elements remote from the shear webs,
relatively thin skin, and little or no taper in plan and front views. The general shear
lag effectiveness factors for such wings should be based on rational analysis or test
data for similar wings, unless the spar web flanges can withstand stresses considerably
higher than those computed by the simple bending theory (refs. 34, 39, and 313).
In a wing having characteristics opposite to those described, general shear lag may be
neglected if the spar flanges can withstand stresses slightly larger than those computed
Figure 313. — Effectiveness of discontinuous stiffener.
160
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
by the simple bending theory. Local shear lag due to discontinuities and cutouts may
be estimated by determining e, from figures 313 and 314, or computed by methods
of reference 313
o
53
u
o
a
•H
u
p
w
o
»
■H
>
•73
?
•H
■P
O
©
w
O
(D
/
v
CutOut
or
Wing Tip
W
\ /
/
/
V
Effectiveness
CQ
V
Figure 314. — Effectiveness of stringer's at cutout.
In using figure 314, L may be taken as 2.5W for conventional constructions em
ploying stiff 45° plywood skin. A more rational value for L, applicable to all grain
directions, may be computed from the following formula which takes into account the
shear rigidity of the skin in relation to the axial load:
1MW
E'A
L =
I
METHODS OF STRUCTURAL ANALYSIS 161
where :
W = width of cutout or tree end.
(7 = effective shear modulus of skin.
t= thickness of skin.
= effective modulus of elasticity of composite section in tension or compression,
as defined in section 2.761.
.4 = total effective area of skin and stiffeners in tension or compression, as defined
in section 2.761.
With the foregoing information available, the wingsection properties may be
computed in a tabular form, such as shown on table 35, the column headings meaning:
(1) Effectiveness factor for item, e.
(2) (a) Geometrical area of item, (A).
(b) Effective area of item, (a ), =eA.
(3) Beam distance of item from reference axis (yi).
(5) Beam moment of area about the reference axis, (ayi).
The location of the X axis, passing through the center of gravity and parallel to the
horizontal reference axis, should next be determined by dividing / col. (5) by /■ col. (2b).
(7) Beam distance of item from the X axis passing through the center of gravity (y).
(9) Beam moment of the area about the X axis, (ay).
(11) Second beam moment of area about the X axis, (ay 2 ).
(13) Individual moments of inertia of items which are of sufficient magnitude to be
included.
The sum of the items in column 9 for all of the wing elements above or all of the
wing elements below the X axis is equal to the static moment of the section Q x . The
sum of items in columns 11 and 13 is equal to the moment of inertia of the wing section
about the X axis. By a similar process, the wingsection properties about the Y axis
can be determined by filling out the remaining columns in table 3 5 pertaining to chord
distances and moments. The X and Y axis are not necessarily the principal axes.
The sum of all of the items in column 15 is equal to the product of inertia of the
section about the center of gravity axes. Careful attention should be paid to the use of
the proper signs in computing the products of inertia and in the subsequent stress calcula
tions.
When effective widths are used for skin in compression, it is evident that the section
properties may change for inverted loads, and in such cases the necessary computations
should be repeated accordingly.
3.1331. Bending stress formulas. The following formulas may be used for the
computation of the bending stresses at any point on the wing section. These formulas
are similar to those described in section 6:6 of reference 315, and permit the stresses
to be computed without determining the principal axes of inertia or the section prop
erties relative thereto.
/' = 
M b y M c x
(3:18)
162
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
in
rH
Product of
Inertia
&
10
d
Ul
1
3
1 Individual 1
O
0) fH
Chord
H
M
to
H
Momenl
Inerl
Beam
g
M
g
M
Oi
H
Second Moment
about CG. Axis
o
g
Beam J
\
Ul
1
y — >
o
H
foment
,G. Axis
Chord
oh
i
First J
about C,
Beam
H
^ — .
00
Distance from
Axis Passing
Through C. G.
Chord
X
' —
* — '
Beam
CD
Moment about
Ref. Axis
Chord
f
«*
in
Beam
c
cd
* —
a
O
Chord
it
to
Distai
Ref,
Beam
as
o
9ATq.0©JJ3
W II
sm©q.i
g &
M M
i "h
■ ■
METHODS OF STRUCTURAL ANALYSIS 163
M b M c ~f M c M b f
where: M b =  ' and M,
j (I xy) S j {I zv)
I x % v ^ x I V
The values of and M c are the values of the bending moments about the X and Y
axes, respectively, used in the section properties computations; the / values are de
termined by the methods outlined in table 35, and the x and y values are the distances
to the points at which the bending stresses are desired.
If the analysis of some of the wing sections indicates that the value of I xV is ap
proaching zero, it is apparent that the reference axes chosen are nearly parallel to the
section principal axes, and the analysis of similar wing sections may be simplified by
omitting the computation of the product of inertia in table 35. The expression for the
stress at any point in this case simplifies to:
f , = _M*_M<y (3;19)
* x 1 y
When desired, the angle of inclination of the principal axes of inertia to the XY
axes is given by the following relation (fig. 312):
Tan#6=y^ff (3:20)
where the values on the right side of the equation are obtained from table 35.
The stress/' computed by the formulas applies directly only to elements having the
elastic modulus selected as basic for the section, and a shearlag effectiveness factor of
1.0. The actual stress/ for other elements is obtained by multiplying/' from the formulas
by the proper effectiveness factor from table 35.
3.134. Secondary stresses in bending elements.
(a) Air loads and bending deflections. Stiffeners are normally subjected to combined
compression and bending. The compression results from the stiffener acting as a part of
the flange material of the entire section. Two of the conditions producing bending in
the stiffeners are : Part of the normal airload on the skin being carried to the ribs by the
stiffeners, and curvature of the stiffeners due to bending deflection of the entire wing.
Allowance for these bending loads may be made by using conservative values for the
allowable compressive stress or, in relatively large rib spacings, by suitable computations
and tests.
(6) Diagonal tensionfield effects. When the wing covering buckles in shear, addi
tional stresses may be imposed on the spanwise stiffeners by the diagonaltension
field effects in the skin. If the initial buckling shear stress is greatly exceeded, it may be
necessary to make additional analyses to account for the increased stiffener stresses.
Shear buckles (diagonaltension fields) in curved skin tend to produce bending or sag
ging of the stiffeners between the ribs. Particular attention should be paid to the possi
bilities of the sagging type of failure in spanwise leadingedge stiffeners, especially when
they are also subjected to combined beam and chord compressive loads. Combined
loading tests or conservative allowable stresses based on simple tests in accordance with
164
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRU( 'TITRES
section 3.1381 should therefore be employed for Dnose spar and similar types of w ings,
(c) Bending stresses due to torsion are discussed in section 3.1370.
3.135. Computation of shear flows and stresses.
3.1350. General. The methods outlined herein are based on the following princi
ples: (refs. 35 and 311).
(1) The shear flow.? producing bending in the wing (direct shear) are distributed
by the various shear elements to each ending element in such a manner as to produce
the increase in axial load per unit of span required by the bending theory. In applying
this principle, use is made of the computations performed in determining the bending
stresses, and the results are affected by the same basic assumptions and limitations.
(2) The shear hows in the various shear elements of a torque box or cell are as
sumed to produce (or resist) torque about a reference point in accordance with the
elementary principles of shear flows, as illustrated in figure 3 15. This assumption is
valid only where: The ribs and bulkheads are rigid in shear in their own plane, particu
larly at concentrated loads; the length of the torque box, or the distance from the section
where a large concentrated torque, applied to the section where it is reacted, is relatively
greater than the crosssectional dimensions of the box ; and where the cross sections of
the wing are free to warp when the wing twists, as in a w ing panel which is so joined to
the center section that only the main beam can transmit bending, the remaining webs
being pinjointed. When any of these conditions are seriously violated, conservative
overlapping assumptions should be made as to the shear in the various elements.
3.1351. Shear flow absorbed by bending elements. The rational methods for
shear distribution first require the determination of the shear flows absorbed by the
individual bending elements which may be determined by one of the following methods:
(1) Spanvrise method. The spanwise method requires the calculation of the total
axial load in each bending element at various stations along the span. The change in
axial load per inch of span at any point is then equal to the shear flow being absorbed
by the element at that point.
This method takes account of beam taper, discontinuities and redistribution of
bending material, and is therefore particularly applicable to complex structures where
these conditions are involved to a considerable degree. The average axial stress, /',
(in terms of tLd "basic" elastic modulus) in each element having small depth compared
to the whole section at a particular station may be obtained by substituting the x and y
coordinates of the centroid of the element in the bending stress formula of section 3. 1331.
The total axial load, P, equals f'Xa, where a is the effective area of the element from
the section properties computations. The shear flow, Aq, absorbed by the element is:
A t =% (3:21,
dP . .
where — is obtained by plotting P against the distance, Z, along the span, and finding
dZ
the slope of the tangent at desired points. Aq may be most conveniently found by
tabular methods, that is: Aq = (P J — P 1 )/ Az, where P t and P 2 are the axial loads at
two adjacent stations and Az is the distance between them. Aq is considered positive
when it tends to increase the tension on an element, proceeding from outboard to in
(b) RESULTANT SHEAR
(o) TWIST OF SHEAR CELL
Symbol*
<?=shear applied per inch of shear element in section view. I Lb. per in.)
>S'= resultant of total shear acting on shear element.
s= length of median line of shear element in section view.
i=thickness of shear element.
f.= shear stress (psi.) = 
t
h= length of chord joining ends of shear element.
o= reference point about which torque is taken.
A = area enclosed between median line of shear element and radii drawn from extremities to 0.
f)= angle of twist of shear cell (radians) per inch of length normal to the section.
G= modulus of rigidity of portion of cell wall.
T= torque about reference point.
Figure 315. — Properties of shear flows.
(b)
Figure 316. — Sign conventions for shear flows.
(2) Section method. The section method determines the shear flow absorbed by
the bending elements by considering one section at a time under the external shears
at that section, with separate corrections, if desired, for the effects of wing taper. This
method is obviously not correct for sections in the vicinity of cutouts on wings having
distributed bending material. It is, therefore, more applicable to wings where the
bending material is concentrated in beams which taper uniformly. The shear flow
absorbed by any bending element is obtained from formulas similar to those for the
METHODS OF STRUCTURAL, ANALYSIS
167
bending stresses (equation 3:18), using the same section properties computations,
as follows:
Ag==a r_^_^] (322)
T= j^f (3:23)
< v 1 xy)
D =
1 (IxvY C3:24)
where :
a = effective area of element.
x and y are coordinates of controid of element from section diagram. Deep ele
ments, such as solid spars, should be broken into smaller elements.
I x , table 35.
I v , table 35.
I zy =y axy, col. 15, table 35.
S6'=the total external beamwise shear (parallel to the Y reference axis for the
section) resisted by the shear elements at the section, positive upward. It may include
a shear correction due to taper in depth, as described in section 3.1352.
S c '=the total external chordwise shear (parallel to the X axis) resisted by the shear
elements at the section, positive rearward. It may include a shear correction due to
taper in plan view.
3.1352. Shear correction for beam taper. When a beam having concentrated
flanges is tapered in depth, a part of the external shear at any station is resisted by
components of the axial loads in the flanges, as shown in figure 317. That part of the
M
shear resisted by the flange axial loads is: AS= — , where M is the moment at the
L o
station and L is the distance from the station to the point where centerlines of the
flanges would meet if prolonged. The shear resisted by the shear elements is then:
S'b = Sb~ A»Sb. If the flange material is distributed over the wing surface a conservative
average taper may be assumed. These corrections for taper should not be used with
the spanwise method of determining shear flow absorbed by bending elements.
3.135 3. Simple D spar. The type of structure considered under this heading is
shown in figure 318. The method described herein is rational in regard to beamwise
shear and torque if the following idealizing assumptions are applicable. The beamwise
bending material is assumed concentrated in flanges at the vertical web; the leading
edge is assumed to be thin, that is, not capable of carrying beamwise bending, and the
leading edge strip (or equivalent material resisting chordwise bending), is assumed to
be located so as not to be affected by beamwise bending nor to incline the principal
168
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
M
&S b > portion of shear resisted by axial loads in flanges of tapered beam
V.
Figure 317. — Shear correction for tapered beam.
axes to the vertical web. As in any single cell, the shear How is statically determinate,
and, under the above assumptions, readily apparent. If the external loads are transferred
to a point on the neutral axis in the vertical web, as shears parallel and perpendicular
to the web, and a torque about the point, as shown in figure 318, the parallel shear,
S'b, is resisted entirely by the vertical web, so that qb = S'b/h, where h is the height
between the centroids of the flanges. The torque, M t , is resisted by the torsion cell,
M t
requiring a shear flow around the periphery: q t = — , where A is the enclosed area.
2A
< d
Figure 318. — Shear in simple Dspar.
The shear S' c is assumed resisted equally by the upper and lower skin, so that:
q c = S' c /2d, where d is the distance from the vertical web to the leading edge strip.
Then: q w (vertical web) =q b — q t ; and qL.E.=qt + q e , with the sign conventions
shown on the diagram.
METHODS OF STRUCTURAL ANALYSIS
169
If the bending material of a Dspar is largely distributed around the periphery in
the form of a thick skin or spanwise stiffeners, the general rational method for single
cells, described in the following, is more applicable.
3.1354. Rational shear distribution.
3.13 540. Single cell — general method. The following method is applicable to
single cell structures having the bending material distributed in the form of a thick
skin or any number of concentrated flanges or stiffeners. However, when such material
is in the form of thick skin, it is assumed divided into strips each of which is considered
a concentrated element. Since the single cell is statically determinate, the elastic
properties of the shear material are not necessarily involved in determining the stress
distribution, although they are required in determining the twist or shear center. For
simplicity, the shear center will not be used in computing shear flows and stresses. Its
location may be readily determined after the shear flows are known. The method of
computing shear flows is briefly outlined as follows: Referring to figure 319, the shear
flow in the main vertical web is considered as an unknown, q,„, and the shear in each
successive shear element around the periphery of the cell is expressed in terms of q m by
successively adding (algebraically) the shear flows, Aq,„ absorbed by the bending
elements. The sum of the torques due to each shear element, about reference point
in the main vertical web, is then computed from the principles of shear flows (figure 315)
and equated to the external torque, M t . This equation is solved for q m , and the numerical
values of the remaining shear flows obtained by successive addition of the Aq values,
as explained. By using a suitable notation, the computations may be reduced to a
simple tabular form as shown on table 36.
Such a notation is described as follows, and is illustrated in figure 319, where
the assumed positive directions of quantities are as shown:
M t = the resultant external moment applied at point when the external shear
Sb and SJ have been transferred to that point.
q m = shear flow in main web.
2ij <?2, q%, etc., are shear flows in successive shear elements numbered clockwise
around the section, as shown.
q n = shear flow in nth shear element.
Aq,, Aq 2 , Aq Jt etc., are shear flows absorbed by bending elements correspondingly
numbered. Aq is positive when it tends to produce tension in the bending element, as
shown in figure 316. It is produced by (or requires) a resultant shear flow directed
away from the element in section view. The values of Aq are assumed to have been
determined by methods such as those of section 3.1351.
A(?„ = shear flow absorbed by nth shear element.
A lt A e , A 3 , etc., are the areas enclosed between shear elements and radii from the
reference point, 0, to centroids of the bending elements.
A = enclosed area of entire section.
T = total torque of shear elements about point 0.
n
y =summation of quantities for elements 1 through n, where n — 1, 2, 3, etc.
T~
N = number of last bending element (lower main flange).
N—1 =number of last shear element (not counting main web).
170
AJSTC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Table 36. — Shearflow computations for single cell.
(1)
(2)
(3)
U)
(5)
(6)
n
t Aq n
• n
= £(2)
l
An
VlAq n
= (4>x(3)
1
2
3
N1
A %
A
A 3
r
N
X
X
N
2>)
1
N1
i
N1
21 (5)
1
N
/ (2) should approximate 0,
Note: Z—
1
N1
^ (4) should approximate total area = A*
1
METHODS OF STRUCTURAL ANALYSIS
171
The expressions for shear now in any element in terms of q m , using sign conventions
of figure 316, are:
Aq,=q,q m > Aq,=q m + Aq,
Aq i = q sl — qi > Aq,=q m + Aq, + Aq s
n
qn = q m + } Ag„ (3:25)
i
Equation (3:25) is represented graphically on diagram (b) figure 319 by a flow q m
n
around the entire section, to which is added flow / Aq n at any shear element to
obtain the total flow q n acting in that element. /
The expression for the total torque of the shear elements about point 0, figure 3
19(a), is:
or
T = )> 2 A n q n
T \~
ir—/ A,,q n , which, from diagram (b)
Li '
of figure 319
(A n > A<?„)
1
Mi
= — (equilibrium of internal and external loads)
Aq m =^) (A n > Aq n )
Z —j— 1
vm 2A A y (i.) A ?B ) (3:26)
Equations (3:25) and (3:26) may be represented in the tabular form shown by
table 36. Equations (3:25) and (3:26) and table 36 are directly applicable to stiff ened
Z)nose type wings if the sign conventions and numbering shown in figure 320 are
employed.
3.13541. Two cell — general method. The following method is an extension of the
general method for single cells. The twocell structure is statically indeterminate since
the division of the total torque between the two cells depends upon their relative torsional
stiffnesses. A shear flow in an element of the front cell and a flow in an element of the
rear cell are therefore considered as unknowns, and the flows in the remaining elements
expressed in terms of these two unknowns. One independent equation is obtained from
/ torques = 0, and another from the fact that the twist of the front cell equals the
twist of the rear cell. The two unknown shear flows are obtained by simultaneous
172
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
(b) GRAPHIC REPRESENT A? IOH OF SHEAR FLOW E<JOATKKS
Figube 319. — Rational shear flow — single cell.
METHODS OF STRUCTUKAL ANALYSIS
173
Fioure 320. — Conventions for stiffenedD nose section.
solution of these equations, and the remaining flows computed by successively adding
or subtracting the shear flows absorbed by the bending elements. The notation is il
lustrated in figure 321, where the following symbols are additional to those described
in section 3.13540 for single cells.
q m = shear flow in main web.
q f = shear flow in first shear element (numbered 0) of front web.
s , s,, s s , . . . s„, are lengths of shear elements.
Co, c,, o, . . . c„, are elastic constants of the shear elements.
c=— , where t e is the effective thickness of the shear element, that is: t e = t, X— ,
tl G
where t t is the geometrical thickness of the element, G,, the shear modulus of the
element, and G the shear modulus of the material considered basic for the section (section
2.52). If a particular element is expected to buckle appreciably in shear, the value of
Gj should be reduced accordingly.
A F = enclosed area of front cell.
A r = enclosed area of rear cell.
A =A F +A B .
n
y = summation of quantities for elements 1 through », where n = l, 2, 3, etc.
1
N = number of upper flange of main web.
M = number of lower flange of main web.
Subscripts f and r refer to front and rear cells, respectively.
Shear flow in any shmr element (see derivation for single cell).
Front cell: ^ —
q. nF = q f +l A 9 „ (3:27)
1
METHODS OF STRUCTURAL ANALYSIS
175
Torque about point 0.
T v
y A„q n , which from diagram (b), figure 321,
Nl
= qA+ qm A R +y (A n > A 9 „)
1
= (External torque)
q f A+q m A K = ~) (A„ ; \q n )
A R M, 1
1 1
Nl n
^f^~^l_ (A„>__A,J (3:29)
which may be written in the form
X g q f +.Y B q m = Z 2 (3:30)
Where X 2 , Y and Z 2 are numerical constants, and q } and q m are unknown quantities.
Consistent deformations. The angle of twist 6 is the same for front and rear cells.
Therefore,
'=^^—4: (3:31)
for each cell, where the summation is taken entirely around the cell. (fig. 315).
1
2G% = . — > qc (3:32)
G is taken out of the summation sign as a constant, since all elements are reduced
to a common basic shear modulus by«use of effective thicknesses. Therefore:
A p A p
qc=j qc
R
q c = R ) qc, which is from diagram (b) of figure 321:
M — 1 Ml n N 1 Nl n
q f y c n +y (c n y h.q n ) — q m c m =Rq, c n +R ) (c n ) Aq n )
1 M M 1
N — 1
+ Kq m y c„ + Rq,„c m (3:33)
M
176 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
or
Ml Nl Nl Nl n
9/0 c n — Fty c„) — q m (e m +~Rc m +Ry__ c„)=R~y (c n ) Aq n )
IT M ~M~ ~~M~~ T~~
Ml
n
(c„> Aq„) (3:34)
1 1
which may be written in the form
X lfJr +Y,q m = Z, (3:35)
The quantities q f and q m are then determined by solving equation (3:30) and 3:35)
simultaneously. The summation terms in these equations may be computed in a form
similar to table 37.
3.13542. Twocell, fourflange wing. If it is assumed for this type of wing (fig.
322) that the skin and web members carry shear only, the general equations given in
section 3. 13541 can be written in the following form :
. M 3__ n
Qr+f 9 m =jj—j > " (A n y A<?„) (3:36)
8 .3 3 n
q,{CoR) f„)q m (c m + Rc m + R,y C B )=#> (c„>  Aq n ) (3:37)
/ / 1
These equations may be expressed as follows :
X £ q f +Y g q m = Z s (3:38)
X 1 q f +Y,q m = Z 1
(3:39)
where:
X, = l (3:40)
Y, = ^f (3:41)
M t 1 '
z?= M~i> {An > _ A «> (3:42)
X,=c a Ry c n f3:43)
V, ^(c m + Rc m +Ry c„) (3:44)
178
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
*' =R > (c»> Aq n ) (3:45)
1 i
Then, solving (3:38) and (3:39) simultaneously,
I±Jt± (3:46)
SHEAR FLOWS SHOWN IN ASSUMED POSITIVE DIRECTION
S b ' = + 100,000 pounds.
&' =  10,000 pounds.
M t =  500,000 inchpounds.
Aq values, as listed in table 37 (determined by sec. 3.1351 (2) )
S, t e , and A values as listed in table 37.
4^ = 2,288 square inches.
= 2,912 square inches.
A =5,200 square inches.
Shear flow values, obtained by substitution of the summations from table 37 in
equations (3:40) to (3:47) are as follows:
q f = 154.3 pounds per inch.
q m =2,140.4 pounds per inch.
The remaining shear flow values are then determined from equations (327) and
(3:28):
METHODS OF STRUCTURAL ANALYSIS
179
q, = — 89 pounds per inch.
q,— —548.1 pounds per inch.
g,, = 36.8 pounds per inch.
3.13543. Shear centers. For some purposes, it is desirable to determine the shear
center of a wing section. As derived herein, the shear center is defined as the point on a
wing section at which the application of a shear load will produce no twist in a differential
length of the structure beyond the section. A point so determined is a true shear center
for the wing as a whole only if the wing is of constant section throughout the span, or
tapers in a manner so that all sections are geometrically similar.
In the following formulas, symbols not expressly defined are the same as in sections
3.13540 and 3.13541.
(a) Single cell. Assume that a V load of value P has been applied to the section and
the values of frqiov the bending elements computed according to section 3. 1351 :
Twist = 6 = =
SAG
/
qc
(3:48)
qc is found by inspection of figure 319 and equation (3 :25), resulting in :
N — l Nl
n
C n +
/
\
(3:49)
1 1 J
Equation (3 :49) is solved for the value of q m which will produce no twist :
Nl n
(Cn
1
1
Nl
(3 :50)
c m +
Cn
1
Let x = the horizontal distance from the origin to the load P for the condition of
no twist. (That is, x = distance to shear center). Since Px = M t , x may be determined
from equation (3:26), as follows:
Nl n_
(3:51)
Pr 1
q "' 2 A A
(A n y \q n )
1
2A
P
Nl
q m +
A
{An
a 9 „:
(3:52)
where q m is from equation (3:50) and other terms are computed as in table 36.
The vertical location of the shear center may be determined, if desired, by applying
a drag load and proceeding as has been shown.
(b) Twocell. It is assumed that a V load of value P has been applied at the shear
180
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
center which is at an unknown horizontal distance x from the origin 0, and that ^q
values corresponding to load P have been computed for the bending elements. Since the
twist of both cells is zero:
1
0/, = O = j> qc (3:53)
R
6« = 0=^> qc (3:54)
Substituting for y qc, according to section 3.13541:
M—l Ml n
'y=0 = g/> c n q m c m +y (c„> Aq n ) (3:55)
11
Nl Nl Nl
n
6«=0 = 9 / > t „+(/„, ( _c n +c m )+) (c n ) Aq n ) (3:56)
M M M 1
Solving equations (3:55) and 3:56) simultaneously for (//and q,„ will give the values neces
sary for the condition of no twist. Since Px is the torsional moment about the origin 0,
this moment and the value of x may be found from the derivation of equation (3:29),
as follows:
M P Ml n
l=^ = q f A + q n A R +y (A n y Aq n (3:57)
1 1
where the values of gyand q m arc from equations (3:55) and 3:56). The vertical location
of the shear center may be determined, if desired, by applying a drag load and proceeding
as in the foregoing.
3.136. Ribs and bulkheads.
3.1360. Normal ribs. Normal ribs (those subjected primarily to airloads), in a
shell wing, receive the airloads from adjacent skin and stiffeners and redistribute them
to the various shear elements of the wing section. The strength of such ribs is always
proven by strength tests, but a picture of the stress distribution is useful in rib design
and m devising suitable test setups. The required airloads, distributed in accordance
with the airfoil chordwise pressure distribution, may be considered as the applied loads
on the rib, and the shear flows applied by the rib to the various wing section shear ele
ments, oppositely directed, as the reactions. Such shear flows may be determined by
performing computations similar to those for the shear flow distribution (using the
section method, sec. 3.1351 (2) ), after resolving the airloads into resultant forces and
a moment, at a convenient reference point.
These conditions may be simulated in a test by constructing a short spnawise
section of the wing in which the test rib at one end forms the loading bulkhead, while a
bulkhead at the opposite end supports the whole section. The spanwise length, and the
METHODS OF STK U( TUKAL ANALYSIS
181
attachment of stiffeners and skin to the support bulkhead, should be such that the rib
loads are not transmitted directly to the support bulkhead by these elements acting as
cantilever beams.
Normal ribs are also subject to a variety of secondary loads, for example: Loads
resulting from their function as compression elements when the skin buckles into diagon
altension fields due to shear; and loads resulting from the axial forces in stiffeners and
skin while the wing is deflected in bending.
3.13600. RibCrushing Loads. Compressive forces in the upper surface material
of the wing, while it is curved upward by bending deflections, produce downward acting
loads in the ribs, while the tensile forces in the lower surface produce upward loads,
thus subjecting the ribs to compression or crushing in the vertical direction. Where an
appreciable portion of the wingbending material is distributed in the form of skin and
stiffeners remote from the beam webs, the ribcrushing loads should be investigated by
methods such as reference 310 or the following :
PL PLM
w= r=eT (3:58)
where :
if = vertical crushing load on rib flange, in pounds per inch of chord.
P = spanwise axial load: in wing surface material due to bending, in pounds per
inch of chord, at given point on wing section.
L = rib spacing, inch.
R = radius of curvature of wing due to bending.
M = bending moment on wing section. (Mb from section 3.1331 may be used as
an approximation.)
/= moment of inertia of wing section. (I x from table 35 may be used as an
approximation.)
E = basic modulus of elasticity used in computing section properties. (Sec. 3.1330. )
3.1361. Bulkhead ribs. Bulkhead ribs are described as those that distribute
loads of appreciable magnitude, other than air loads, to the wingsection shear elements;
for example, fuselage, landing gear, and fuel tank reactions. Such loads, as well as the
airloads, may be considered as external loads applied to the rib, and the shear flows
applied by the rib to the shear elements, oppositely directed, as the reactions. Here,
however, one or more of the conditions required by the shearflow theory (sec. 3.135)
will generally be violated. For example, a larger amount of shear may be absorbed by
the elements nearest a concentrated load, depending on their rigidity relative to that of
the bulkhead. Conservative overlapping assumptions should therefore be made.
Bulkhead ribs may also perform the function of redistributing shear among the
shear elements of a wing wherever some of these elements are discontinued or bending
elements redistributed. The shear flows from the outboard wing section may then be
considered as the applied loads on the rib, and the shear flows applied to the inboard
section, oppositely directed, as the reactions.
Likewise, at a rib where any wing element carrying an appreciable axial load
changes direction, the axial loads in the inboard and outboard portions of such an ele
ment should be resolved into components parallel and perpendicular to the plane of
182
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
the rib. The resultant of the components in the plane of the rib may then be considered
as a load applied to the rib, with reactions supplied by the wingsection shear elements
as described previously.
As a result of the bulkhead analysis, it may be necessary to revise the shear distri
bution determined in the general shear analysis (sec. 3.135) for local conditions.
3.137. Miscellaneous structural problems.
3.1370. Additional bending and shear stresses due to torsion. The corner flanges
of a box beam are theoretically free from axial (bending) stresses under a pure torque
loading, if the cross sections are free to "warp" as the box twists. However, in a shell
wing where more than one beam is continuous through the fuselage, either directly or
through an equivalent structure, bending stresses will be induced in the corner flanges
since the opposing action of the opposite wing will restrain the root sections from warp
ing. Additional shear in the short sides of the box is also induced at restrained sections.
In wings not subjected to unusual torque loads and in which the torque cells are
continuous and enclose a large part of the sectional area of a reasonably thick wing,
the bending stresses at the root due to torsion should be small compared to the total
bending stresses for the loading conditions producing maximum bending in the wing.
Analytical methods for computing the bending stress due to torsion in various
types of box wings are described in references 38 and 312. Where the shear rigidity
of one wall of a box wing is greatly reduced by a cutout, the wing torsion should be
assumed to be carried as differential bending in the spars in the region of the cutout.
Rational solution of the general case is given in reference 36.
Wings in which the torsional stiffness of the torque cells is relatively small because
of the small enclosed area or because of many large cutouts may be conservatively
designed as independent spar wings. The effect of the torque cell in relieving the critically
loaded spar by transferring part of the load to the other spars may, however, be esti
mated according to reference 37.
3.1371. General instability. Reference to section 3.1381 shows that the column
length of spanwise stiffeners is generally taken equal to the rib spacing. Such an as
sumption is valid only when the ribs act as rigid lateral restraints for the stiffeners at
the points of intersection. If the ribs lack rigidity in their own planes, allowing the
stiffeners to deflect laterally, the axial compressive loads in the stiffeners tend to further
increase such deflections because of the resulting eccentricities. If the rib rigidity is
too low relative to the axial stiffener (or skin) compressive loads, a state of equilibrium
will not be reached, and the ribs and stiffeners will collapse simultaneously. In con
ventional wings with full depth ribs, the condition described above, known as general
instability usually need not be considered. If shallow ribs (at tank bays and wheel
wells) or trusstype ribs having shallow flanges are used in wings where a large part of
the bending compressive loads are carried in surface material remote from the wing
beams, analysis or tests for this condition should be made (ref. 314).
3.138. Strength determination. The analytical determination of the strength of
the structure is based on a comparison between the computed internal stresses, and the
allowable stresses obtained by static test or calculated from the material properties by
methods such as those of chapter 2. In order that the computed margins of safety so
obtained may represent the strength of the structure with respect to the specified ex
ternal loads, as accurately as possible, all conditions and assumptions on which both
METHODS OF STRUCTURAL ANALYSIS
183
the internal and allowable stresses are based should be reviewed, and any necessary
adjustments or allowances made, prior to the final comparison showing the margins of
safety. Such allowances may be made by arbitrarily increasing the originally computed
internal stresses or decreasing the allowable stresses, in the light of the review.
Some of the factors to be considered in the strength determination are discussed
under the following subsections.
3.1380. Buckling in skin. For a structure in which the major portion of the
compressive loads due to bending are intended to be resisted by the skin, with the
shape being maintained by comparatively light reinforcing structure, the critical
buckling and ultimate stresses for the skin, whichever is lower, should be considered
as the allowable stress. When buckling does not occur, the ultimate allowable stresses
may be computed by the methods of sections 2.60 and 2.61. The criteria of sections
2.70, 2.80, and 2.82 may be used as guides in predicting the occurrence or nonoccurrence
of buckling, but the strength of such structures should be substantiated by static tests
of the complete structure, or of a closely similar structure, to ultimate load, because
of the uncertainties of buckling phenomena.
For structures in which the supporting and stiffening members are capable of
withstanding a major portion of the compressive loads, buckling of the skin does not
necessarily result in failure, as discussed in the following subsections on stiffened panels
and shear elements. Sharply curved skin panels have much higher critical buckling
stresses than flat panels of the same dimensions, but failure in curved panels usually
occurs immediately after buckling begins.
3.1381. Compression elements. Where secondary stresses, such as those de
scribed in sections 3.1330 (5), 3.134, and 3.1370 have not already been taken into ac
count, a reasonable increase in internal stresses should be assumed for critical elements
affected thereby. Although wood will yield slightly in compression, tending to relieve
the highly stressed fibers, elements which have undergone some crushing in compres
sion may fail at unexpectedly low tensile stresses when the load is reversed.
When light span wise stiffeners are used to reduce the size of the skin panels rather
than to resist the wing bending loads, they need not be designed to withstand the stresses
which would be assigned to them as isolated structural elements by the bending theory,
provided that such stiffeners are designed to accommodate themselves to the spanwise
shortening of the compression side of the wing without failing. At locations remote
from the spars, this can be accomplished by making the stiffeners sufficiently flexible
so that they can bow between the ribs without failing. Such stiffeners may tend to
separate from the skin, however, unless special precautions are taken. At locations
adjacent to highly stressed spar flanges this accommodation may be obtained by using
a cross section and material such that local crippling and crushing failure will not occur.
3.1382. Stiffened panels. In structures where the skin is expected to buckle
below ultimate load and the reinforcing structure is designed accordingly, the allow
able compressive stresses may be obtained from section 2.76 or from tests on stiffened
panels.
(a) Effective widths. In both the allowable and the internal stress computations,
an effective width strip of skin adjacent to each stringer is assumed fully effective in
compression. The width is often selected arbitrarily, and it is sometimes assumed
that the value selected makes little difference so long as the value used in the section
184
AN (J BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
properties computations is consistent with that used in computing allowable stresses
from the total load supported by a test panel This assumption would be true if the
upper and lower bending material of the wing consisted only of two symmetrical panels
(with the same effective widths in tension as compression) but it may lead to some error
if the bending material is not structurally symmetrical and the usual methods of com
puting section properties are used. Therefore, for structures in which the skin carries
a considerable portion of the bending load, the effective widths should be determined
as accurately as possible, either by theoretical methods, such as those of section 2.760,
or by accurate straingage measurements on the test panels. The effective width, 2w,
of plywood panels, is usually expressed as a strip that is considered to act at a stress
corresponding to that of the unbuckled plywood at the same deformation as the stiffener.
(Sec. 2.760.) The effective width of metal panels is usually expressed as a strip acting
at the same stress as the stiffener. The basis for the effective widths indicated in a
particular analysis should, therefore, be clearly stated.
(b) Allowable compressive stresses. In determining the allowable compressive
stress, the various possible modes of failure discussed in section 2.7610 should be con
sidered. When the allowable stress is computed by section 2.761, the stiffener plus
effective width of skin is considered as one composite element having an effective mod
ulus of elasticity E'. This procedure was arranged to facilitate checking the stress in
any ply or fiber of either plywood or stiffener. Such a composite element may be con
sidered as one item in the sectionproperties computations (sec. 3.1330), where e t will
E'
equal — basic. The computed internal stress, /, for comparison with the allowable
E
will then be : / =/' X e, where /' is the fictitious basicmodulus stress obtained by the
bending formulas in section 3.1331, and e is the total element effectiveness factor in
accordance with section 3.1330 (5).
When the ribs are sufficiently rigid in their own planes (sec. 3.1371) the column
length of the stiffened panels is taken as equal to the rib spacing. In regard to the
columnfixity coefficient to be used in conjunction with this column length, it is noted
that typical structures show a general tendency to bow inward in the bays between
ribs, but a few bays will tend to bow outward. Where one bay bows in and the next
out, a fixity of approximately c = 1.0 is developed, depending on the rotational fixity
furnished by the ribs and the degree of buckling and plate or curvature effect of the
skin. A value of c = 1.5 may be assumed if the stringers are fixed to ribs having appre
ciable bending stiffness in a vertical plane parallel to the stringers. Higher values
should not be used in design unless substantiated by tests on a complete structure.
In flatendedpanel tests, a value of c = 3.0 or more is usually developed. The
results of such tests must therefore be corrected to the fixity value used in the design
of the structure.
(c) Combined stresses. A convenient method of considering the effects of combined
compression and shear in stiffened panels is the stress ratio or interaction curve method,
that is, R m +R a n = 1.0, where R c is based on the allowable compressive stress discussed
in paragraph (b), and R s is based on the strength of the panel in pure shear.
The exponents m and n may be assumed equal to 2.0 for panels which are sub
stantially flat, but not more than 1.0 for sharply curved panels, such as in Dnose spars,
unless tests are made under combined loads to determine points on the interaction
METHODS OF STRUCTURAL ANALYSIS
185
curve. For Dnose spars, tests to ultimate load should be made. A portion of the
spar of sufficient length to eliminate end effects, may be used in such tests.
3.1383. Tension elements. Tension elements of wood yield very little, compared
to metals, before reaching their ultimate strength. Unaccountedfor secondary stresses
or unconservative assumptions in the stress analysis are therefore likely to cause fail
ures. Since the plywood skin, stiffeners, and spar flanges on the tension side of a wing
may not reach their ultimate strengths at the same time, the stresses in each element
should be determined and compared with the corresponding allowables. For plywood
having the face grain parallel or perpendicular to the spanwise direction, the modulus
of elasticity for use in determining section properties and internal stresses may be
obtained from section 2.52, or table 29, and the allowable tensile stress from section
2.601, and table 29. For plywood having the face grain at an angle to the spanwise
direction, the spanwise modulus of elasticity may be obtained from section 2.56. For
the special case of plywood with face grain at 45° to the span, the value of E may be
obtained as described in section 2.56110. The allowable tensile stress for such 45°
plywood may be obtained from section 2.611 and table 29.
When the plywood on the tension side does not buckle due to shear, which is usually
the case on a wing (sec. 2.702), the condition for failure under combined tension and
shear may be determined by stress ratios in accordance with section 2.613.
3.1384. Shear elements. When the shear flow, q, has been determined, the internal
shear stress is obtained by dividing q by the actual thickness of the element, even though
an effective thickness based on relative moduli of rigidity was used in the shear dis
tribution analysis. The allowable shear stress values given by section 2.72 are directly
applicable to beam webs and allow for the effects of the beam bending stresses near the
flanges.
These allowable shear stresses should also be applicable to substantially flat wing
skin panels in the same range with respect to buckling. The ultimate strength of
curved panels in shear must at present be obtained from tests on specific structures as
described in section 3.1382 (c), since buckling usually precipitates failure.
3.2 FIXED TAIL SURFACES. The procedures applicable for use in the stress
analysis of fixed tail surfaces (fin and stabilizer) are analogous to those described in
section 3.1 for the analysis of wings. The nature of the applied loads is necessarily similar
in that the source is principally aerodynamic and the spanwise and chordwise distribu
tions of the same are similar to those over wing surfaces. The loads resulting from
inertia effects require a consideration similar to that employed in the analysis of wings.
The dependence of the applicable type of analysis upon the structural arrangement
of the material is also similar to that encountered with wings and this consideration is
treated in section 3.1. The strength of the structure is determined by comparison of the
calculated internal loads and stresses with the allowables which are obtained either from
tests or from the information given in chapter 2. The determination of the strength of
shell structures, including reinforced shells, is presented in detail in section 2.138.
3.3. MOVABLE CONTROL SURFACES. The movable control surfaces are ordi
narily comprised of the ailerons, elevator, and rudder. The analysis of each of these
surfaces is fundamentally the same basic problem. Each movable surface consists of
an airfoil free to rotate about a hinge axis fixed on the supporting structure except as
restrained by the control system at its attachment point (control horn). The essential
186
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
structure is made up of the :
(1) Airfoil surface (fabric or plywood plating) upon which the air forces act and are
transmitted through
(2) Surface attachment means (lacing, nails, or glue) to the
(3) Ribs. The ribs transfer the air loads through shear and bending to the
(4) Main beam and
(5) Torque tubes. The beam and torque tube are supported by the fixed surface
structure at the
(6) Hinges where the transverse shear is transmitted to the fixed surface. The torque
tube carries the torque resulting from the air loads and hinge support reactions to the
(7) Horn, where it is balanced by the control system reactions.
A satisfactory analysis should include a check of the plating material (fabric, ply
wood) under the imposed design pressure loading. Unit pressure loadings, consistent
in magnitude with those encountered over deflected control surfaces should be considered
in such a check. The strength of the surface attachments should be checked in combina
tion with that of the surface material itself. The most satisfactory method of determining
the strength of such structural items is by "blowoff tests" of panels representing the type
of construction employed (simulating rib spacing, surface attachments) when subjected
to test pressures representing the design loadings. Critical surface pressures are usually
negative (tending to blow the surface outward).
Ribs may be considered as cantilever beams supported at the main beam or torque
tube and supporting the pressure loading over the area extending approximately midway
to adjacent ribs. Here again static tests of representative" structures constitute the pre
ferred basis for proof of satisfactory strength.
The main beam and torque tube should be checked under the shear, bending, and
torsional loads resulting from the rib loadings, and the reactions at the hinge supports
and the control horn. When the main beam or torque tube is continuous over three or
more hinge supports, the deflection of the fixed surface or wing under flight loads should
be taken into account by introducing suitable deflections of the supports into the three
moment equations or by conservative overlapping assumptions. Irregularities and dis
continuities of such structures are often encountered because of the cutouts necessary
for the control surface hinges. Care should be exercised to provide adequate strength
and rigidity in way of such cutouts by means of proper reinforcing and by use of con
servative assumptions both as to stresses developed and stresses allowed. This is es
pecially necessary in wood structures because of the inherent inability of wood to equalize
stress concentrations through considerable plastic deformation.
3.4 FUSELAGES.
3.40. General. Most of the commonlyused types of wood fuselage construction
fall within one of the following:
( 1 ) Fourlongeron type.
(2) Reinforced shell (semimonocoque) type.
(3) . Pure shell (monocoque) type.
Examples of these types are included in the sketches shown herein under the pertinent
subheadings. A particular airplane fuselage need not necessarily be confined to one
type of construction but may employ any applicable combination. For example, the
METHODS OF STRUCTURAL ANALYSIS
187
stiffenedshell type may revert to the fourlongeron type in way of large cutouts such as
cockpit openings, or bomb bays.
3.41. FourLongeron Type. The treatment of the fourlongeron type is somewhat
analogous to that of the Dsection and singlecell shells as described in section 3.13 with
the additional simplification that results from the inherent symmetry of the typical
fuselage section. In both, the material effective in bending is concentrated into a small
number of locations and the section properties for use in a bending analysis may be
calculated in the normal manner as based upon such an assumption. The plywood shell
material will actually contribute in some indeterminate extent to the bending strength
of such fourlongerontype sections as are illustrated in figures 323 and 324. However,
it is probable that, on the compression side, this contribution will be limited to approxi
mately that corresponding to the buckling load for the plywood panels as determined
from the transverse frame spacing, panel thickness, species, arrangement of plies, and
curvature according to the methods described in chapter 2. In this type of construction,
the unit deformation corresponding to the maximum design stress in the longerons very
probably exceeds by far that corresponding to the buckling stress of the adjacent plywood
material and of that farther removed from the neutral axis. Also, without curvature
and without longitudinal stringers between longerons and the smaller plywood panel
expanses and greater buckling stresses resulting therefrom, the design shearing stress
in the sides of the fourlongerontype section will also probably exceed the buckling
values by a considerable amount.
Both of these tendencies lead to the conclusion that it is satisfactorily conservative
to neglect the contribution of the plywood shell to the bending properties in cases where
the buckling stresses of such shell material is considerably exceeded by the longeron
stresses and shear web stresses calculated on the basis of zero contribution (fig. 323).
In any event, the optimum contribution of the shell material that could be expected
would be that corresponding, on the compression side, to the buckling stress of the panels
and, on the tension side, full effectiveness. In this connection, the designer's attention
is directed to the existing knowledge of the behavior of thin panels subsequent to buck
ling. With flat panels and panels of slight curvature (that is, those in which the con
tribution of curvature to the buckling load is not significant) a load approximately equal
to the buckling load is maintained after buckling. With thick plates of considerable
curvature (that is, those in which the contribution of curvature to the buckling load is
appreciable) the load tends to drop off after buckling. In such panels, rupture is also
much more likely to result at buckling. For these reasons, it is desirable that under the
ultimate design loads, the stresses resulting in such a portion of a compression flange
do not exceed the critical buckling stresses. On the tension side, the contribution of the
plating should be taken as that corresponding to an equivalent area of the plywood
flange in terms of the longeron material (fig. 324). For purposes of calculation, the
equivalent effective area (or thickness) of the tension plywood flange would be equal to
t X— where t = plywood thickness, E, = modulus of elasticity of longeron material in a
E,
direction normal to the section, and modulus of elasticity of plywood material in a
direction normal to the section. These definitions are different from those used in
chapter 2.
188
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
A. ILLUSTRA TIN 6 SHEA/? INTENSITIES
DUE TO VERTICAL LOAD
REJLH
SHEAR INTENSITY
due to V load
r  V
B. ILLUSTRATING SHEAR INTENSITIES
DUE TO SIDE LOAD
A^LOtidtkOH Af£A)
[L0N6ERON
AfiEA)
n = SLA,b,+A?h > '] .
5 ZI ft
z  SA z b t 4
h 21 h
SHEAR INTENSITY DUE TO T DROVE Q, = J—
fr 2A
RESULTANT SHEAR INTENSITY a, = a + a + a
Hv 5s OT
BENCH NG STRESS f k = ~ 
NOMENCLATURE
S= SIDE LOAD (TRANSVERSE SHEAP) AT SECTION
V = VERTICAL LOAD (VERTICAL SHEAR) AT SECTION
r= TORQUE ABOUT INTERSECTION OF REF. AXIS WITH PLANE OF SYMMETRY OF SECTION
% = SHEAR INTENSITY ( LBS. PER INCH RUN)
M= BENDING MOMENT ABOUT N. A. AT SECTION (+ M CAUSES COMPRESSION IN
UPPER AND R.H. FLANGE! MATERIAL  LOOKING FORWARD)
1= MOMENT OF INERT/A ABOUT N.A. OF EFFECTIVE BENDING AREA
A= AREA ENCLOSED BY SHELL
x= DISTANCE OF BENDING MATERIAL FROM YY NA.
y = DISTANCE OF BENDING MATERIAL FROM /X NA.
Figure 323. — Fourlongeron fuselage — plating ineffective in bending.
METHODS OK STRUCTURAL ANALYSIS
189
COMPRESSION j/.
SIDE
TENSION
SIDE
*£ct.xiL if BUCKLED AT DESIGN LOAD
t A IF UNBUCKLED AT DESIGN LOAD
IHEFFtCllve
A. PARTIALLY BUCKLED SHELL
Y
B. UNBUCKLED SHELL
Fcr = PANEL BUCKLING STRESS
F = LONGERON ALLOWABLE STRESS
E z  MODULUS Of ELASTICITY OF PLYWOOD NORMAL TO SECTION
E, = Modulus of elasticity of longeron normal to section
Figure 324. — Fourlongeron fuselage — plating effective in bending.
190
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
In determining the optimum effectiveness of the compression plywood material,
it is emphasized that the total load carried by the material would be approximately
limited to the buckling load rather than being proportional to the total load upon the
section. If it is considered permissible for the subject panel to buckle at the design
load, the effective thickness for use in computing section properties may be taken as
approximately t \ —\ ( — Y defined in figure 324. If it remains unbuckled the cor
\Fj\yJ , E \
responding effective thickness may be taken as t yj^ J. The applicable procedure must
be checked by computing the actual stress in the plating and comparing it with F Ccr .
The resultant external applied loads on the section in question should be resolved into :
(1) Vertical shear (in plane of symmetry).
(2) Transverse shear (at reference point determined by fig. 323).
(3) Moment about each of the principal section axes.
(4) Torque about reference axis (for example, the intersection with the plane of
symmetry of the transverse reference axis defined by fig. 323).
The plywood panels (sides, top, and bottom) can be considered to carry the shear upon
the section, both that due to the vertical and transverse loads and that resulting from
torsion. When the flange material is concentrated in the longerons, the shear intensity
(pounds per inch run) can be considered constant between adjacent flanges. The shear
intensity, and thus the shear stress, may then be determined by figure 323 without
the use of the shear center. Such center may be determined, if desired, by the methods
of reference 311. Calculations made in connection with the application of the thinshell
theory, developed primarily for use with isotropic metal materials, should be modified
to account for variations in the modulus of rigidity (G) for the various wood panels as
affected by wood species, direction of grain, relative thickness and arrangement of plies,
according to the methods described in chapter 2.
If the shell thickness, curvature, and frame spacing are such that the buckling
stresses will not be exceeded under conditions of maximum oading, the section properties
may be calculated usfhg the full shell area as modified to correspond to equivalent
longeron material, that is, the proportionate amount of effective shell material, in terms
E
of longeron material, is equal to — as previously described. When the section prop.
E,
erties are thus calculated on the basis of longeron material, the bending stress in the
longerons is determined in the usual manner.
U=^ (3:59)
Where yi is the distance of the longeron material from the neutral axis. The bending
stress in the plywood material, however, is determined as
(3:60)
Where yi is the distance of the subject material from the neutral axis.
The possible variety of assumptions made to facilitate analysis can be considerable
and will, to a large extent, be determined by the individual details of the problem
together with the designer's experience, judgment, and discretion. An adequate sup
METHODS OF STRUCTURAL ANALYSIS
191
plementary statictest program is required, and it is also essential that the assumptions
used in converting the test data into allowable loads and stresses be duplicated in the
stress analysis of the flight article.
3.42. ReinforcedShell Type. This type of construction is very broad in nature
and covers the field extending from the longeron type with large longerons and thin
shell to the type approaching the pure shell, that is, small longitudinals and thick shell.
3.421. Stressedskin fuselages. Stressedskin fuselages usually are structures of
the reinforcedshell, singlecell type, and the basic methods of wing analysis, as described
in section 3.13 generally can be applied directly to the analysis of such fuselage struc
tures. Due to variations of the type of loading and certain other structural problems,
however, it is considered advisable to review the fuselage analysis problem as a separate
subject.
Unless a fuselage of this nature conforms closely to a previouslyconstructed type,
the strength of which has been determined by test, a stress analysis is not considered
as a sufficiently accurate means of determining its strength. The stress analysis should
be supplemented by pertinent test data. Whenever possible, it is desirable to test
the entire fuselage for bending and torsion, but tests of certain component parts may
be acceptable in conjunction with a stress analysis.
3.422. Computation of bending stresses. Prior to computing the bending stresses,
it is necessary to compute the fuselagesection properties. As was previously recom
mended in section 3.13, it is considered advisable to make a sketch of the fuselage
section considered. This sketch should indicate all of the material assumed to be
effective. Figure 325 is a sketch of a fuselage cross section of the subject type.
On the tension side of the fuselage the skin material may be assumed to be acting
as discussed in the following, while, on the compression side, only the effective width
of skin (section 2.76) adjacent to the stiffener should be assumed to be acting. In
general, the modulus of elasticity of the plywood plating will differ from that of the
stiffener material. Account of this fact must be taken in calculating the section prop
erties. This may be done by converting the actual area of the plating on the tension
side into that of equivalent stiffener material, either in terms of equivalent thickness
or equivalent widths — the latter being somewhat analogous to the effective width as
used on the compression side. The geometrical shape of the section contour together
with the arrangement and spacing of stiffener material will dictate which method of
treatment is analytically simpler or more accurate. The proportionate effectiveness of
E,
the plating material in tension may be taken as — as described previously under
section 3.42. E *
Proper account for wood species, plywood grain attitude and arrangement, and
veneer thicknesses should be taken into account according to the procedures described
under section 2.76. The determination of bending stresses by means of the formula
implies the assumption of plane sections remaining plane sections. Hence, the cal
culated stresses in the plating material, as based upon section properties determined
by conversion of plating material into equivalent stiffener material, must also be modified
E
in the ratio — . The resulting corrected stresses in the plating must be compared with
192
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
ILLUSTRATING TREATMENT OF MATERIAL
EFFECTIVE IN 3 ENDING A 30UT XX AXIS
Figure 325. — Reinforced shell fuselage.
the allowable tensile stresses in the plating material as described in section 3.1383.
Such a check should always be made of plywood material adjacent to highly stressed
stiffener material, even where the contribution of such plywood material has been
completely neglected in the determination of section properties. In order to account
for the effect of shear on the effective widths for stiffeners on the side of the fuselage,
it is advisable to compute the effective widths for all stiffeners on the compression side
on the basis of a panel edge stress corresponding to the allowable stress of the stiffener,
rather than the actual stress to which it may be subjected. It is customary to assign
to each stiffener and adjacent skin an item number. Prior to actual computations, the
designer should make an estimate of the neutral axis location, thereby dividing the
elements into those on the compression side and those on the tension side. After the
location of the true centroid of the section has been determined, the designer will be
able to check the accuracy of his original assumptions as to neutralaxis location.
It usually will be found that no corrections for axis location are necessary if the
final axis is located relatively close to the one originally assumed. A procedure similar to
that described in section 3.1330 will be found convenient for computing the section
properties. Distances and moments originally are taken from some conveniently lo
cated reference axis. The sum of moments about the reference axis, after being divided
by the sum of the areas in the section, gives the location of the neutral axis of the sec
METHODS OF STRUCTURAL ANALYSIS
193
tion. Distances of the items from the neutral axis are then determined. The sum of
the products of the areas located on either side of the neutral axis multiplied by the
distances to the neutral axis is equal to the static moment of the section about the neutral
axis, Q, and the sum of second moments of all of the elements of the section is equal to
the moment of inertia of the section, I. Where the axial loads produce appreciable
values of bending moments on the fuselage, these moments should be included in the
bending moment, M, which is used to obtain the axial stresses due to bending.
Critical stresses commonly are assumed to occur at the stiff eners located farthest
away from the neutral axis on the compressive side, and the stresses in these stiffeners
resulting from bending are computed by the equation, M being the critical moment
at the section and y being the distance of the stiffener from the neutral axis.
Although the bending theory indicates that the outermost fibers are the critical
ones, it will often be found that stiffeners located near the top or bottom, on the shoulders
of the section, are the ones which are liable to fail during tests if the skin buckles in
shear. Such stiffeners usually are subjected to comparatively large direct stresses due
to bending and, at the same time, may act as the stiffeners of the tensionfield shear
material transmitting the shearing stresses to the outermost stiffeners. Unless these
stiffeners are of sufficiently large proportions to resist the bending loads imposed by
the tensionfield effects, failures of these stiffeners may occur at loads smaller than
anticipated.
3.42 3. Computation of shearing stresses. The bending material in fuselage
sections usually is distributed in such a manner that under symmetrical loadings it
may be safely assumed that each side carries half of the vertical shear load, and the cor
. . VQ
responding shearing stress, f s , at any point is equal to , where V = the shear force act
2tl
ing on the section, Q = static moment about the neutral axis of the areas located between
the outermost fibers and a horizontal line through the point under consideration, / =
moment of inertia of the section, and / = thickness of the skin at the point under con
sideration.
The sum value, Qx (table 35), should be used for determining the maximum
shearing stresses that occur at the neutral axis of the fuselage. Although these methods
pertain to the analysis of the fuselage for a shear load applied in a vertical direction,
similar methods can be employed for a shear load applied horizontally, such as a side
load on the vertical tail. If the structure is not too unsymmetrical about a horizontal
plane, the shear center for application of the horizontal load may be estimated, using
overlapping assumptions. If a more exact solution of shear distribution is desired,
the methods of section 3.135 may be used. The total shear stress (or intensity) at any
section is that obtained from the superposition of the component shear stresses (or
intensities) resulting from vertical loads, transverse loads, and torsion.
Although the fuselage structure as a whole should be checked for the shear distribu
tion as determined in the foregoing, it is recommended that certain sections of the
fuselage be checked for other types of shear stress distribution that may be more in line
with the actual load application. At the point of wing attachment to the fuselage, for
example, very large loads are transmitted to the fuselage frame through the attachment
194
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
fitting. It is reasonable to assume that high shearing stresses will be present near this
fitting, gradually tapering to the extremity of the frame. Although this assumption is
not in agreement with the conventional bending theory, it is recommended that it be
considered in design to allow for probable shear concentrations.
T
Torsional shear stresses can be computed by the conventional formula /„ =
%A t
and should be combined with the stresses due to direct shear. The tendency of tension
fields to sag the stiffeners also should be considered. Because similarity seldom exists
between the geometric properties of different airplane structures, it is difficult to draw
conclusions from one design as to the allowable shear stresses to be used for other
designs. It is usually necessary, therefore, to conduct panel tests on representative curved
shear panels.
3.43. PureShell Type. By definition, the pure shell or monocoque type of structure
incorporates no longitudinal stiffening members. Hence, the ultimate strength of such a
structure may be taken as the critical buckling strength of its elements. As described
in chapter 2, the buckling strength of a plywood panel may be estimated from its thick
ness, frame or stiffener spacing, wood species, arrangement of plies, and curvature.
It is generally desirable that no portion of the structure become buckled prior to the
application of the design load. In such a case, in. the calculation of section properties,
the material may be considered fully effective and the stresses determined according
to the fundamentals of mechanics.
In a section such as shown in figure 326B, however, certain portions may become
buckled at low loads without materially affecting the final loadcarrying capacity of the
total section. This may be exemplified by the buckling of flat panels on the compres
sion side while the major portion of the total flange material is unbuckled by reason
of its difference in curvature or thickness. It is generally satisfactorily conservative
to omit the buckled material from consideration. Such, a partially buckled structure
must, of course, be adequately stiffened by frames.
3.431. Monocoqueshell fuselages. The basic principles of the design of thin
walled cylinders, as discussed in ANC5 sections 1.63 and 1.64 can be applied to the
design of monocoque fuselages. The monocoque portion of the fuselage structure usually
is restricted to certain sections of the fuselage, such as the tail portion. In the center
and in the forward portions of the fuselage, the reinforcedshell type of construction,
which is more suited to the region where cutouts are present, generally is used. Careful
attention should be given to that part of the fuselage structure where two types of con
struction join. Adequate length and attachment of the reinforcing members to the shell
should be provided. At the points where the monocoque section stops at cutouts,
transfer of the load from monocoque portion to the stiffeners around the cutout should
be investigated carefully. (Ref . 319. )
Tests of monocoque fuselages have demonstrated that the strength is dependent
to some extent on the smoothness of the plating. The designer should, therefore, be
certain that the methods of assembly of monocoque fuselages in the shop will produce
a satisfactory product. Where small margins of safety are present and when the effects of
load concentrations have not been taken into account conservatively, strength tests
should be carried to the full ultimateload values, because the type of failure in this
type of structure usually is elastic, and the appearance of the structure under proof
METHODS OF STRUCTURAL ANALYSIS
195
Y
A. UNBUCKLED (FULLY EFFECTIVE)
UNBUCKLED
B. PARTIALLY BUCKLED
Figure 326. — Pure shelltype fuselage.
load may be no indication of the ability of the structure to carry the required ultimate
loads.
3.44. Miscellaneous Fuselage Analysis Problems. Each new type of fuselage
may present a new set of problems which has not occurred in other types. It is recom
196
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
mended, therefore, that every new type of fuselage be tested at least to the critical ulti
mate loads to determine the presence of possible stress concentrations and other effects
which could have been overlooked in the most careful design. Some of the analysis
problems which are somewhat common to all types of fuselages are discussed in the fol
lowing sections.
3.441. Analysis of seams. The allowable loads of the seams should be computed
and compared with the loads imposed by direct tensile stresses, by shear stresses, by any
tension field effects of the shear stresses, and by combined stresses due to the action of
all these stresses.
3.442. Analysis of frames and rings. The analysis of the fuselage frames consti
tutes a separate problem. Many manufacturers have adopted certain standard methods
of frame analysis, which, although not necessarily mathematically rigorous for the types
of the structures considered, have produced satisfactory designs. A general discussion
of some of these methods is given.
3.4421. Main frames. Main frames are primarily for the purpose of distributing
into the fuselage such concentrated loads as the loads from wings, tail surfaces, or
landing gear, and those resulting from the local support of items of mass. Mainframe
structures usually are of the redundant type and their analysis is based on the principles
of least work and related or equivalent methods such as strain energy, column analogy,
moment distribution, or joint relaxation (ref. 32 and 33).
Figures 327 A, B, and C show a fuselage main frame under a symmetrical loading
condition. The loads from the wing (or landing gear) are shown applied at the applicable
fittings and are resisted by shear forces in the fuselage skin. To agree with the elementary
bending theory, these shear intensities should be distributed so as to conform to the
or — values of the fuselage section, as applicable, giving a distribution of shear
forces of the type shown in figure 327 A or B. Some designers take into account the
fact that, due to concentration of load where the frame is attached to the wing, the shear
is carried mostly by the adjacent fuselage skin and the shear resistance of the skin is
reduced arbitrarily, somewhat in proportion to its distance from the point of concentrated
load application. This would yield a shear force distribution of the type shown in figure
327 C. In such cases, the fuselage skin should also be checked for the high stresses
indicated.
The ordinary method of frame analysis is strictly applicable to frames the de
flections of which are not restricted by the fuselage skin. Actually, the frame deflections
may become quite pronounced and the outward deflections are resisted by double
curvature effects in the fuselage skin or by the support of adjacent frames. This action
of the skin is equivalent to an introduction of inwardacting loads resisting the frame
bending and hence to a reduction of frame stresses to smaller values than those indicated
by an analysis based upon shear distributions as described. The present development of
the theory does not indicate quantitatively just what allowance can be made for this
reduction of stresses. It is recommended, therefore, that the frame analysis be conducted
by the methods similar to the ones indicated.
Where relatively deep frames are used, the moments induced by the wing de
flections may become important and should, therefore, be analyzed.
METHODS OF STRUCTURAL ANALYSIS
197
ft: * ^ IS »U
<v ^ cj 5 >* ^
^ * 9c
=c o ^
5r ^ ^
<m y> ^
—
198
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
3.4422. Intermediate frames. Intermediate frames are provided to preserve the
shape of the fuselage structure, to reduce the column length of the stiffeners, and
to prevent failure of the structure due to general instability. They are subjected to
several types of loading; such as, those due to tension fields in the skin, to fuselage
bending, to transfer of shear to the fuselage plating. Many of these loads are compara
tively small and often tend to balance each other. For these reasons the design of
intermediate frames is often based on the experience of the designer or on semiempirical
methods. In the case of large airplanes, however, it becomes of considerable importance
to design frames of this type to provide suitable stiffness for the prevention of general
instability.
3.443. Effects of cutouts. Effects of cutouts usually are allowed for by omitting
the bending material affected by the cutout from the computation of the section prop
erties. For shearing stress computations in the location of regularly spaced cutouts,
such as windows, the shear stress in the skin between cutouts may be taken as equal
to that computed on the assumption that no cutouts are present and then increasing
this value by the ratio of distance between cutout centerlines to the distance between
the cutouts. Such treatment, although quite arbitrary, has served satisfactorily with
metal material. Because of the inherent lack of ductility in wood and its inability to
deform plastically and redistribute stresses adjacent to local concentrations such as
cutouts, the incorporation of large calculated margins of safety is recommended in such
locations.
In case of large openings, such as the cabin door cutouts, allowance for bending
stress redistribution usually is made by modifying the section properties by omitting the
material affected by the cutout. For computation of the shearing stresses, it may be
assumed that the direct shear load is carried through that side of the fuselage not con
taining the cutout. The couple resulting from this unsymmetrical reaction in way
of the cutout can be assumed to be resisted by a shear couple consisting of equal and
oppositely directed transverse reactions in the top and the bottom of the fuselage. The
redistribution of the shear stress, as assumed, can be achieved best if bulkheads are
provided on both sides of the door. Where only one main bulkhead is provided (at
only one end of the cutout ) shear redistribution on the other side of the cutout must
be accomplished by the frame under the flooring and by the intermediate frames. Refer
ence 319 describes the basic theory and recommended methods of determining the
shear distribution in the plating about cutouts, and also the corresponding effect of the
cutouts upon the loads in the stringers and frames.
3.444. Secondary structures within the fuselage. Often the designer is faced with
the problem of existence of a secondary beam structure inside the main fuselage or hull
structure. This secondary structure may consist of keels or keelsons in a flyingboat hull,
or of the floor supporting structure or nosewheel retracting tunnel in a fuselage. If this
type of structure is analyzed separately under the specified local loads alone, the stress
distribution may not correspond to the distribution that will be obtained with it acting
in conjunction with the rest of the fuselage structure. The designer should make certain
that the combined effects of the two structures are in agreement and that the action of
the structure as a whole is consistent with expected deformations.
3.45. Strength Determination. The strength of the structure is determined by
comparison of the calculated internal loads and stresses with the allowables obtained
METHODS OF STRUCTURAL ANALYSIS
199
either from tests or from the information given in chapter 2. The determination of the
strength of shell structures, including reinforced shells, is presented in detail in section
3.138.
3.5 HULLS AND FLOATS. The analysis of hulls and floats may be treated in a
manner similar to that used with fuselage structures, the chief difference being in the
manner in which the major external loads are applied, that is, by direct contact with
the water in the form of normal pressures. Fundamentally, hull and float structures
consist of :
(1) Bottom plating — that, in contact with the water, is loaded by the normal pres
sures developed in landing, takeoff, or buoyancy, and transfers such loads to the —
(2) Bottom stringers — that support the plating and transfer the plating loading
to the supporting —
(3 ) Frames — that in turn carry the water loads through to the —
(4) Main longitudinal girder — or general structure. Consideration is given to the
fact that water causes concentrated local loads on float and hull bottoms that may
reach intensities considerably above the average loading and may be applied at different
times and for different durations to different portions of the bottom structure. For
these reasons the strength requirements for design of the bottom plating are specified
as more severe than those for stringer design. The bottom stringer strength require
ments are, in turn, more severe than those for complete frame design. The specified
loads as applicable to the design of the general structure are in general of lesser local
intensities but are consistent with the design airplane accelerations and total reactions.
3.51. Main Longitudinal Girder. This structure may consist of a centerline truss
or bulkhead girder to which the frames, deck, side and bottom plating are attached.
Or, the deck, side, and bottom plating and stringers plus other longitudinal material
connecting to, and capable of acting with, the skin plating and stringers may be con
sidered as a reinforced shell which comprises the longitudinal girder. In such a structure
the frames not only serve to transmit the water loads to the general structure, but pro
vide the transverse and circumferential stiffening for the shell. The effective longitudinal
members ordinarily considered to take the bending loads consist of: keel, bottom string
ers, keelson, chine, deck, and stiffeners. The effective shear material consists of side,
deck, and bottom plating. The analysis assumptions, calculation of section properties,
and determination of normal and shearing stresses applicable to the longitudinal girders
are in general as described under section 3.4 for fuselage analysis.
3.52. Bottom Plating. Thin plating, when subjected to sufficient normal pressures
will either rupture or deflect excessively and take a permanent set. In hulls and floats
this latter effect is known as "wash boarding," and in an acceptable structure should not
be allowed to occur at loads below those corresponding to yieldpoint loads. For this
reason the design criteria established by the procuring or certificating agency in general
consists of specification of certain designbottompressure loadings in conjunction with
the permissible permanent deformations at the specified pressure loadings. Permanent
deformation is measured at the center of the plating panel, between stringers and relative
to the stringers, in a direction normal to the plane of the plating.
The analytical determination of bottomplating stresses and deflections is exceed
ingly difficult of accurate attainment, and the problem of design calculation methods,
including the basis for allowable stresses, hence lends itself most readily to treatment by
200
ANC BULLETIN— DESIGN OE WOOD AIRCRAFT STRUCTURES
testing procedures. Test panels representative of (1) the plating species, thickness and
plywood type, (2) the stringer spacing, frame spacing, and panel aspect ratio, and (3)
method of edge support and type of edge restraint should be tested under normal pres
sures, and the applicable strength criteria (ultimate strength, arbitrary or true yield,
and permanent deformation) determined. Test data may be interpreted and converted
in light of the calculation procedures described in chapter 2.
In such a treatment, two of the influential factors that determine the calculated
stresses and deflections are (1) type of edge support, and (2) aspect ratio of panel.
Clamped or fixed edges assume the plating to be restrained from any rotation at the
edges, the neutral plane of the plywood maintaining zero slope. In simply supported
edges, conversely, a possibility of rotation of the neutral plane of the plywood at the
edge is implied. The plates actually encountered in the design of floats and hulls lie
somewhere between fixed and supported edges and may be considered as elastically
restrained. The maximum stress in a plate with fixed edges occurs at the long edges,
whereas it occurs in the middle of a plate with simply supported edges. It follows from
this that a slight deflection or twist of the fixed edges of a plate will decrease the stress
close to the edges where it is a maximum and increase it near the middle where it was,
however, originally much less. Bottom stringers are not ordinarily very stiff torsionally
and constitute a type of support bordering upon the simply supported edge. On the
other hand, keel, keelson, and chine members are necessarily quite stiff torsionally, as
well as laterally, in that they must be well gusseted to adjacent frames and, forming
the edge of the plate panels, must be stiff enough to prevent lateral deflections. Hence,
the analytical treatment under both limiting conditions of edge support should give
considerable guidance in design.
The ratio of frame spacing to stringer spacing ordinarily exceeds 3.0 and hence, the
aspect ratio of the plating panels for use in design can usually be taken as infinite.
3.5 3. Bottom Stringers. As previously mentioned, the bottom stringers serve to
transfer the bottom plating normal loads to the transverse frames. They may be con
sidered in general as continuous beams supported at the frames with a running load per
unit of length equal to the stringer spacing times the intensity of bottom pressure.
Under the ordinary conditions of uniform pressure, frame and stringer spacings, the
symmetry of loading would permit the consideration of the stringer as a uniformly loaded
continuous beam over fixed supports. This would lead to a design bending moment in
the stringer:
where W = stringer transverse loading, in pounds per inch
and L = support spacing, in inches.
The extreme probability of loadings other than symmetrical and the finitely elastic
nature of the support restraint leads to the use of the more conservative specification
of the design bending moment as :
(3:61)
10
(3:62)
When the conditions of loading are definitely different from these assumptions (that is,
when the pressure varies, when the stringer is not continuous, or when the support has
METHODS OF STRUCTURAL ANALYSIS
201
unusual restraint characteristics) the stringer should of course, be designed to the local
conditions specifically applicable.
It is rational to consider a portion of the plating adjacent to a stringer as effectively
contributing to the section properties of the stringer. It is important that the same
assumptions as to plating effectiveness be used in converting test data into allowable
stresses as is used in the analysis of the flight article under the specified loads.
As well as being analyzed for the specified design bottompressure loading, the
plating and stringer combination should be checked for the conditions in which it is
both subjected to direct water loads and also forms a part of the effective flange material
of the general longitudinal girder structure. In such conditions, the stresses resulting
from the bottom pressures consistent with the loadings on the general structure are
superimposed upon the stresses incurred as a portion of the flanges of the general structure.
3.54. Frames. Hull and float frame design differs from ordinary fuselage frame
design principally in the nature of the applied loads which result from direct water
pressures. Each frame is considered to take the bottom loadings applied to the plating
and stringer combination structure in the area adjacent to the frame. Such loaded area
extends approximately onehalf of the frame spacing to both sides. The bottom loads
are usually transmitted from the stringers directly to the frame in the area between the
chines. The assumptions as to the nature and magnitude of the balancing reactions in
the form of shear in the side and deck plating may be patterned after those used in
fuselage frame design.
In almost all instances, frame analysis involves the problem of the application of
the fundamental methods of least work and in this respect may be treated in a manner
similar to that employed with analogous fuselage frames. The probability of unsym
metrical loading applications on Vbottom hulls and floats in takeoff and landing is
quite high. For this reason the procuring or certificating agency specifies in all instances
certain unsymmetrical designloading conditions. Such loading conditions are often
critical for the design of frames, and hence the analysis of frames loaded in this manner
should be given the utmost care and consideration.
3.5 5. Strength Determination. The strength of the structure is determined by
comparison of the calculated internal loads and stresses with the allowables obtained
either from tests or from the information given in chapter 2. The determination of the
strength of shell structures, including reinforced shells, is presented in detail in section
3.138.
3.6. MISCELLANEOUS. Treatment of the wing, fuselage, hull, tail, and control
surfaces does not complete the stress analysis of the airplane structure. In airplanes of
wood construction, however, it is considered that these same structural components
constitute nearly all of those in which the use of wood is significant and in the analysis
of which the physical properties of wood will enter as an important factor. Hence, for
such reasons and as explained in section 3.00, treatment of the detailed analysis problems
related to the remaining important airplane structural components will not be included
herein. Such components would include, for example, landing gear, engine mount, con
trol systems, fittings, and joints. The determination of the design load applied to each
individual wood structural element of a joint (mechanical joint or glue joint), or fitting
attachment, may be determined by basic principles of mechanics and machine design.
Where it would significantly affect the distribution of the design load, the nonisotropic
202
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
nature of wood, which results in the strength and elastic characteristics being dependent
upon the relation between the directions of the load and of the grain, should be taken
into account by a rational treatment or provided for by conservative arbitrary assump
tions. The design load thus determined for such an element should be compared with
the allowable load defined by the applicable portions of chapter 2 (principally section
2.9). The designer is referred, in general, to the many existing tests, technical papers,
and publications which adequately handle such miscellaneous analysis problems.
METHODS OF STRUCTURAL ANALYSIS
203
REFERENCES FOR CHAPTER 3
(31) Akerman, J. D. and Stephens, B. C.
1938. POLAR DIAGRAMS FOR SOLUTION OF AXIALLY LOADED BEAMS. Jour. Aero. Sci. July,1938
(32) Cross, Hardy
1930. the column analogy. Univ. of Illinois Eng. Exp. Sta. Bulletin 215.
(33)
1930. analysis of continuous frames by distributing fixedend moments. Proc.
A.S.C.E. May, 1930.
(34) Erlandsen, O. and Mead, L.
1942. a method of shearlag analysis of box beams for axial stresses, shear stresses,
and shear center. N.A.C.A. Advance Restricted Report.
(35) Hatcher, Robert S.
1937. rational shear analysis of box girders. Jour. Aero. Sci. April, 1937.
(36) Ebner, Hans
1934. torsional stresses in box beams with cross sections partially restrained
against warping. N.A.C.A. Tech. Memo. 744.
(37) Kuhn, Paul
1935. ANALYSIS of twospar CANTILEVER wings with SPECIAL REFERENCE TO TORSION
and load transference. N.A.C.A. Tech. Rept. 508.
(38) Kuhn, Paul
1935. bending stresses due to torsion in cantilver box beams. n.a.c.a. tech.
Note 530.
(39)
1938. APPROXIMATE STRESS ANALYSIS OF MULTISTRINGER BEAMS WITH SHEAR DEFORMA
TION of the flanges. N.A.C.A. Tech. Rept. 636.
1939. loads imposed on intermediate frames of stiffened shells. N.A.C.A. Tech.
Note 687.
1939. SOME elementary principles of shell stress analysis with notes on the use
of the shear center. N.A.C.A. Tech. Note 691.
(310)
(311)
(312)
1942. a method of calculating bending stresses due to torsion. N.A.C.A. Advanced
Technical Report. (Restricted)
(313) Kuhn, P. and Chiarito, P.
1941. lag in box beams, methods of analysis and experimental investigations.
N.A.C.A. Tech. Note 739. (Restricted)
(314) LUNDQUIST, E. AND SCHWARTZ, E. B.
1942. A STUDY' OF GENERAL INSTABILITY OF BOX BEAMS WITH TRUSS TYPE RIBS. N.A.C.A.
Tech. Note 866. (Restricted)
(315) Niles, A. S. and Newell, J. S.
1938. airplane structures. Second edition John Wiley and Sons, Inc.
(316) Rowe, C. J.
1924. application of the method OF least WORK TO redundant structures. A.C.I.C.
495.
(317) Schwartz, A. M. and Bogert, R.
1935. ANALYSIS OF A STRUT WITH A SINGLE ELASTIC SUPPORT IN THE SPAN, WITH APPLICA
TIONS TO THE DESIGN OF AIRPLANE JURY'STRUT SYSTEMS. N.A.C.A. Tech. Note 529.
(318) Shanley, P. R. and Cozzone, F. P.
1941. unit method of beam analysis. Jour. Aero. Sci. April, 1941.
(319) Wagner, H.
1937. THE stress distribution in shell bodies and wings as an equilibrium problem.
N.A.C.A. Tech. Memo. 817.
204
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
CHAPTER 4. DETAIL STRUCTURAL DESIGN
TABLE OF CONTENTS
4.0 GENERAL 205
4.00 Introduction 205
4.01 Definitions 205
4.010 Solid Wood 205
4.011 Laminated Wood 205
4.012 Plywood 205
4.013 Highdensity material 205
4.1 PLYWOOD COVERING 205
4.10 General 205
4.11 Joints in the Covering 205
4.12 Taper in Thicknessof the Covering .206
4.13 Behavior Under Tension Loads . .208
4.14 Behavior Under Shear Loads 208
4. 1 5 Plywood Panel Size 209
4.16 CutOuts 210
4.2 BEAMS 210
4.20 Types of Beams 210
4.21 Laminating of Beams and Beam
Flanges 213
4.22 Shear Webs 213
4.23 Beam Stiffeners 213
4.24 Blocking 215
4.25 Scarf Joints in Beams 215
4.26 Reinforcement of Sloping Grain . .215
4.3 RIBS 216
4.30 Types of Ribs 216
4.31 Special Purpose Ribs 216
4.32 Attachment of Ribs to the
Structure 218
4.4 FRAMES AND BULKHEADS 220
4.40 Types of Frames and Bulkheads. . 220
4.41 Glue Area for Attachment of
Plywood Covering 220
4.42 Reinforcement for Concentrated
Loads 220
4.5 STIFFENERS 220
4.50 General 220
4.51 Attachment of Stringers 222
4.52 Attachment of Intercostals 222
4.6 GLUE JOINTS 222
4.60 General 222
4.61 Eccentricities 222
4.62 Avoidance of EndGrain Joints. . .223
4.63 Gluing of Plywood Over Wood
Plywood Combinations 224
4.64 Glui ng of High Density Material .224
4.7 MECHANICAL JOINTS 224
4.70 General 224
4.71 Use of Bushings 224
4.72 Use of High Density Material 224
4.73 Mechanical Attachment of Ribs. .226
4.74 Attachment of Various Types of
Fittings 226
4.75 Use of Wood Screws, Rivets, Nails,
and SelfLocking Nuts 226
4.8 MISCELLANEOUS DESIGN
DETAILS 227
4.80 Metal to Wood Connections 227
4.81 Stress Concentrations 227
4.82 Behavior of Dissimilar Materials
Working Together 228
4.83 Effects of Shrinkage 228
4.84 Drainage and Ventilation 229
4.85 Internal Finishing 230
4.86 External Finishing 231
4.87 Selection of Species 232
4.88 Use of Standard Plywood 232
4.89 Tests 233
4.9 EXAMPLES OF ACTUAL DESIGN
DETAILS 233
DETAIL STRUCTURAL DESIGN
4.0. GENERAL.
4.00. Introduction. Detail design practice is constantly changing and current
good practice may at any time be obsoleted by some new treatment of a particular
design problem. Therefore, the examples presented on the following pages represent
only the current methods used in handling problems of design details. It should be
remembered, however, that many of these methods have withstood the test of time,
having been used since the first introduction of wood aircraft.
4.01. Definitions. The following definitions explain a few general terms which are
sometimes confused by the wood aircraft designer. Other terms requiring definition
are explained as they appear in the text.
4.010. Solid Wood. Solid wood or the adejctive "solid" used with such nouns as
beam or spar refers to a member consisting of one piece of wood.
4.011. Laminated Wood. Laminated wood is an assembly of two or more layers
of wood which have been glued together with the grain of all layers or laminations
approximately parallel.
4.012. Plywood. Plywood is an assembled product of wood and glue that is
usually made of an odd number of thin plies (veneers) with the grain of each layer at an
angle of 90° with the adjacent ply or plies.
4.013. HighDensity Material. The term "high density material" as used through
out this chapter includes compreg or similar commercial products, heat stabilized wood,
or any of the hardwood plywoods commonly used as bearing or reinforcement plates.
4.1 PLYWOOD COVERING.
4.10. General. Nearly all wood aircraft structures are covered with stressed ply
wood skin. The notable exceptions are control surfaces and the rear portion of lightly
loaded wings. Shear stresses are almost always resisted by plywood skin, and in many
cases, a portion of the bending and normal loads is also resisted by the plywood.
4.1 1. Joints in the Covering. Lap, butt, and scarf joints are used for plywood skin.
When plywood joints are made over relatively large wood members, such as beam
flanges, it is desirable to use splice plates, often called aprons or apron strips, regardless
of the type of joint. It is desirable to extend the splice plates beyond the edges of the
flange so that the stress in the skin will be lowered gradually, thus reducing the effect
of the stress concentration at this point. Splice plates (fig. 41) can be made to do
double duty if they are scalloped corresponding to rib locations so that they may act as
gussets for the attachment of the ribs.
Scarf joints are the most satisfactory type and should be used whenever possible.
Scarf splices in plywood sheets should be made with a scarf slope not steeper than 1
in 12 (fig. 42). Some manufacturers prefer to make scarf joints in such a way that the
external feather edge of the scarf faces aft in order to avoid any possibility of the air
flow opening the joint.
205
206
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Figure 41. — Use of Splice Plate.
Acceptable Better
Scarf Joint Made Directly Upon Scarf Joint Made
Solid or Laminated Flange Upon Splice Plate
Figure 42. — Scarf Splices.
If butt joints (fig. 43) are made directly over solid or laminated wood members,
as over a spar or spar flange, experience has indicated that there is a tendency to cause
splitting of the spar or spar flange at the butt joint under relatively low stresses. A
similar tendency toward cleavage exists where a plywood skin terminates over the
middle of a wood member instead of at its far edge.
Lap joints (fig. 44) are not recommended because of the eccentric load placed
upon the glue line. If this type is used it should be made parallel to the direction of
airflow, only, for obvious aerodynamic reasons.
4.12. Taper In Thickness of the Covering. Loads in the plywood covering usually
vary from section to section. When this is so, structural efficiency may be increased by
tapering the plywood skin in thickness so that the strength varies with the load as closely
as possible (fig. 45). To taper plywood in thickness, plies should be added as dictated
DETAIL STRUCTURAL DESIGN
207
POOR POOR BETTER
SKIN TERMINATES AT THE BUTT JOINT DIRECTLY OVER SPLICE PLATE 15 GLUED TO
MIDDLE OF THE FLANGE . SOLID OR LAMINATED WOOD THE FLANGE AND THE BUTT
HA5 SAME EFFECT A5"A" JOINT 15 MADE ONTOP OF IT
Figure 43. — Butt Splices.
AA BB
Plan View of Wing Panel Lap Joint on a Rib at a Lap Joint Where It
Chordwlse Station Between Beams Croesee Beam Flange
Figure 44. — Lap Splices.
by increasing loads. In doing so, the plywood should always remain symmetrical. For
example, plywood constructed of an odd number of plies of equal thickness can be
tapered, and at the same time maintain its symmetry, by adding two plies at a time.
This method is suitable for bag molding construction. Stress concentrations should be
avoided by making the change in thickness gradual, either by feathering or by scalloping.
In bag molding construction, the additional plies are often added internally so that the
face and back are continuous.
By Feathering
By Soalloping
Figure 45. — Tapering Plywood in Thickness.
208
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
When flat plywood is used, the usual method of tapering skin thickness is to splice
two standard plywood sheets of different thicknesses at an appropriate rib station
with a slope of scarf not steeper than 1 in 12 as shown in figure 46.
Figure 46. — Scarfing Plywood of Different Thicknesses.
4.13. Behavior Under Tension Loads. Because the proportional limit in tension
and the ultimate tensile strength of wood are reached at approximately the same time,
plywood skin loaded in tension must be designed very carefully. Observation of various
static test articles has indicated that squarelaid plywood (plywood laid so that face
grain is parallel or perpendicular to the direction of the principal bending stresses) has a
tendency to rupture in tension before the ultimate strength of the structure has been
reached (fig. 47). Diagonal plywood, however, seldom ruptures before some other
structural member fails. The reason for this behavior is probably due partly to the fact
that none of the fibers of the diagonal plywood are in pure tension. The failure under
tension load at 45° to the grain is almost entirely a shear failure, and the fibers, which
have a definite yield beyond the proportional limit in shear, may undergo enough in
ternal adjustment to permit the plywood to deflect with the structure until some other
member becomes critically loaded. Squarelaid plywood does not yield because some
of its plies will fail in tension almost immediately after the proportional limit has been
reached. This drawback of squarelaid plywood becomes less important when the skin
is designed to carry a greater proportion of the bending loads. For the limiting case of a
shell structure without flanges, squarelaid plywood is preferable.
Rupture of the skin is also influenced by its relative distance from the neutral axis.
If the beam or beams are located so that part of the skin is appreciably farther from the
neutral axis than the beam flanges, the skin is more likely to have a premature failure
than if the flanges are located at the greatest outer fiber distance. Such a condition
is illustrated by wing spars placed at the 15 and 65 percent chord wise stations of a nor
mal airfoil.
Where the spanwise plies of plywood covering are of a wood species different from
the beam flanges, it is, of course, desirable that such plies have a ratio of ultimate tensile
stress to modulus of elasticity equal to or greater than that of the beam flanges.
4.14. Behavior Under Shear Loads. Diagonal plywood (face grain at 45° angle
to the edge of the panel) is approximately five times stiff er in shear than squarelaid
plywood and somewhat stronger. When shear strength or stiffness is the controlling
design consideration, diagonal plywood should be used (sec. 4.22).
DETAI Jj STRUCTURAL DESIGN
209
Figure 47. — Static Test Wing Showing Tension Failure of Plywood Covering.
4.15. Plywood Panel Size. In certain cases the size of plywood panels is dictated
by the magnitude of directly computable stresses. These occur, for example, in spar
webs, Dtube nose skin, and fuselage side panels subjected to high shear. In many other
cases, however, the design loads are insignificant. It then becomes necessary to choose
combinations of skin thickness and panel size which will stand up under expected handling
loads, have acceptable appearance, and aerodynamic smoothness. The typical values
given in table 41 have been employed by experienced manufacturers.
Table 41. — Typical panel sizes
Material
Thickness
Panel Size
Location
Remarks
Inch
Mahogany, yellowpoplar core
Do
Do
Do
Do
Do
Do
Mahogany
Do
Yellowpoplar
Inch
12 by 24 maximum
by 10^
10 by 12
5 by 9
11 by 20
10 by II
24 or 36 square
7 by 14
18 by 24
14 by 36
Wing skin.
do
do.
Leading edge skin.
Vertical fin
Stabilizer
Fuselage
Leading edge skin . . . .
Fuselage
Wing aft of 50 percent
chord.
Spanwise face grain.
Some curvature required.
Spanwise face grain.
Just aft of cabin.
210
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
4.16. CutOuts. When cutouts are made in plywood skin for windows, inspection
holes, doors, or other purposes, sharp corners should be avoided, and for all but small
holes in lowstressed skin, a doubler should be glued to the skin around the cutout.
For some types of cutouts a framework can be installed to carry the shear load and
doublers need not be used (figs. 48, 49, and 410).
Doubler
AA
Poor
Bett»r
Figure 48. — Plywood CutOuts.
Stop Nuts Riveted to Doubler
Stop Nuts Set in Routed lftood Ring
X
Cover Plate
Section AA
Section BB
Figure 49. — Two Methods of Attaching Inspection Hole Covers.
4.2. BEAMS.
4.20. Types of Beams. The types of beams shown in figure 411 have been used
frequently as wing spars, control surface spars, floor beams and wing ribs. The terms
"beam" and "spar" are often used interchangeably and both are used in this chapter.
The woodplywood beams (box, I, double I, and C) are generally more efficient
loadcarrying members than the plain wood types (plain rectangular and routed). A
discussion of the relative merits of these various beam types is presented in succeeding
paragraphs.
The box beam is often preferred because of its flush faces which allow easy attach
ment of ribs (sec. 4.32). The interior of box beams must be finished, drained, and ven
tilated. Inspection of interiors is usually difficult. The shear load in a box beam is
Figure 410. — Methods of Carrying Torsion Loads Around Hinge CutOuts in Control Surfaces.
212
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
BOX *T DOUBLET
*C" PLAIN RECTANGULAR ROUTED
Figure 411. — Types of Beams.
carried by two plywood webs. By checking shear web allowables by the method given
in section 2.72, it will be seen that for the same panel size a plywood shear panel half
the thickness of another will carry less than half the shear load which can be carried
by the thicker panel.
The preceding statement points to an outstanding advantage of the Ibeam since
its shear strength is furnished by a single shear web rather than the two webs required
of a box or double Ibeams. Also, the Ibeam produces a more efficient connection be
tween the web and flange material than the box beam in cases where the web becomes
buckled before the ultimate load is reached. This is because the clamping action on
the webs tends to reduce the possibility of the tension component of the buckled web
cleaving it away from the flange.
The double Ibeam is usually a box beam with external flanges added along that
portion where the bending moments are greatest. This type allows a given flange area
to be concentrated farther from the neutral axis than other types.
The Cbeam affords one flush face for the flush type of rib attachment but it is
unstable under shear loading. Cbeams are generally used only as auxiliary wing spars
or control surface spars.
Plain rectangular beams are generally used where the saving in weight of the wood
plywood types is not great enough to justify the accompanying increase in manufactur
ing trouble and cost. This is usually the case for small wing beams, controlsurface
beams, and beams that would require a great deal of blocking.
DETAIL STRUCTURAL DESIGN
213
Routed beams are somewhat lighter than the plain rectangular type for the same
strength but not so light as woodplywood types. Usually this small weight saving
does not justify the increase in fabrication effort and cost.
In determining the relative efficiency of any beam type, reduction in allowable
modulus of rupture due to form factors must be considered.
4.21. Laminating of Beams and Beam Flanges. Beam flanges and plain rectangu
lar and routed beams can be either solid or laminated. A detailed discussion of methods
of laminating beams and beam flanges is presented in section 2.4 of ANC Bulletin 19,
Wood Aircraft Inspection and Fabrication (ref. 24).
Since the tension strength of a wood member is more adversely affected by any
type of defect than is any other strength property, it is recommended that all tension
flanges be laminated in order to minimize the effect of small defects and to avoid the
possibility of objectionable defects remaining hidden within a solid member of large
cross section.
4.22. Shear Webs. Although squarelaid plywood has been used extensively as
shear webs in the past, the present trend is to use diagonal plywood (fig. 412) because
it is the more efficient shear carrying material (sec. 4.14).
It is desirable to lay all diagonal plywood of an odd number of plies so that the face
grain is at right angles to the direction of possible shear buckles. In this way the shear
web will carry appreciably higher buckling and ultimate loads because plywood is much
stiffer in bending in the direction of the face grain and offers greater resistance to buckling
if laid with the face grain across the buckles (fig. 413). This effect is greatest for 3ply
material.
Figure 414 illustrates various methods of splicing shear webs. If the splices are
not made prior to the assembly of the web to the beam, blocking must be inserted at the
splice locations to provide adequate backing for the pressure required to obtain a satis
factory glue joint.
4.23. Beam Stiffeners. Shear webs should be reinforced by stiff eners at frequent
intervals as the shear strength of the web depends partly upon stiffener spacing (fig.
415). In addition to their function of stiffening the shear webs, the ability of beam
stiffeners to act as flange spreaders is very important and care must be exercised to
provide a snug fit between the ends of the stiffeners and the beam flanges. External
stiffeners for box beams are inefficient because of their inability to act as flange spreaders.
Stiffeners are usually placed at every rib location so that the web will be stiffened
sufficiently to resist ribassembly pressures.
Squarelaid Plywood
Diagonal Plywood
Figure 412. — Types of Shear Webs.
214
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
the lace ply of the web ^
Figure 4—13. — Orientation of face grain direction of diagonal plywood shear webs.
Butt Joint with Simple Scarf Joint Diagonal Scarf Joint
Splice Plate
Figure 414. — Methods of Splicing Shear Webs
5tiffener of solid or laminated^ — ladder type stiffener; ^— ply wood web wfth corner
wood; lightening holes are often wood vertical stiffeners blocks ■, holes are often
drilled to reduce weight oh the are separated br "plywood cut in web to reduce
piece may be routed strips weight
Figure 415. — Typical Stiff eners for I and Box Beams.
DETAIL STRUCTURAL DESIGN
215
4.24. Blocking. Any blocking;, introduced for the purpose of carrying fitting loads
(fig. 416), should be tapered as much as possible to avoid stress concentrations. It is
desirable to include a few crossbanded laminations in all blocking in order to reduce
the possibility of checking.
Poor
Better
I o o
! o
i
» o
' o o
Figure 416. — Bearing Blocks in Box Spar.
4.5. SCARFJOINTS IN BEAMS. The following requirements should be ob
served in specifying scarf joints in solid or laminated beams and beam flanges:
1. The slope of all scarfs should be not steeper than 1 in 15. The proportion of end
grain appearing on a scarfed surface is undesirably increased if the material to be spliced
is somewhat crossgrained, and the scarf is made "across" rather than in the general
direction of the grain (fig. 417). For this reason it is very desirable that the following
note be added to all beam drawings showing scarf joints:
Where cross grain loithin the specified acceptable limits is present, all scarf cuts should
be made in the general direction of the grain slope.
A
/A/CORRECT
8
INCORRECT
C CORRECT
Figure 417. — Relationship Between Grain Slope and Scarf Slope.
2. In laminated members the longitudinal distance between the nearest scarf tips
in adjacent laminations shall be not less than 10 times the thickness of the thicker
lamination (fig. 418).
In addition to the previously mentioned specific requirements, it is recommended
that the number of scarf joints be limited as much as possible; the location be limited
to the particular portion of a member where margins of safety are most adequate and
stress concentrations are not serious; and special care be exercised to employ good
technique in all the preparatory gluing, and pressing operations.
4.26. Reinforcement of Sloping Grain. Where necessary tapering produces an
angle between the grain and edge of the piece greater than the allowable slope for the
216
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
L
I
"t" is the thicknesB of the
thicker lamination.
1
Figure 418. — Minimum Permissible Longitudinal Separation of Scarf Joints in Adjacent Laminations.
particular species, the piece should be reinforced to prevent splitting by gluing plywood
reinforcing plates to the faces (fig. 419).
Figure 419.— Solid Wing Spar at Tip.
4.3. RIBS.
4.30. Types of Ribs. Rib design has changed very little for several years. See
N.A.C.A. Technical Report 345 (ref. 223). The more common types are the plywood
web, the lightened plywood web, and the truss. The truss type is undoubtedly the most
efficient, but lacks the simplicity of the other types.
For fabriccovered wings the ribs are usually one piece with the cap strips con
tinuous across the spars. When plywood covering is used the ribs are usually con
structed in separate sections (fig. 420).
Continuous gusset stiffen cap strips in the plane of the rib. This aids in preventing
buckling and helps obtain better ribskin glue joints where nail gluing is used because
such a rib can resist the driving force of nails better than other types. Continuous
gussets (fig. 421) are more easily handled than the many small separate gussets other
wise required.
Any type of rib may be canted to increase the torsional rigidity of a structure such
as a woodframework, fabriccovered control surface (fig. 422).
Diagonals loaded in compression are more satisfactory than diagonals loaded in
tension since tension diagonals are more difficult to hold at the joints.
4.31. Special Purpose Ribs. Where concentrated loads are introduced, as at
landing gear or nacelle attachments, bulkheadtype ribs can be used to advantage.
DETAIL STRUCTURAL DESIGN
217
, — RIB CAP5 CONTINUOUS ACR055 5PAR5
LIGHTENED PLYWOOD WLB TYPE.
Figure 420. — Typical Wing Ribs.
Figure 421. — Rib Employing Continuous Gussets.
Figure 422.— Control Surface Employing Canted Ribs.
218
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
When this is the case, the rib acts as a chordwise beam, and the principles presented in
section 4.2 will apply (fig. 423).
Bi
A— 1
Figure 423. — Special Purpose Ribs.
4.32. Attachment of Ribs to the Structure. In general, ribs are glued to the adja
cent structure by means of corner blocks, plywood angles or gussets, or in special cases,
by some mechanical means. These are all shown in detail in figures 424, 425, 426,
427, 434, and 439.
Figure 424. — Typical Rib Attachments to Flush Surface Beams.
Although the attachment of ribs to Ibeams may complicate the rib design, many
engineers believe that the mechanical shear connection obtained by notching the ribs
so that the end may be inserted between the Ibeam flanges is an advantage since the
shear connection is not dependent upon quality of the glue joint between the rib and
DETAIL STRUCTURAL DESIGN
219
the beam shear web. This type of connection is shown in figure 425. The rib vertical
also acts as a stiffener for the beam shear web and as a flange spreader.
LYWOOD PLATE
THESE CORNER BLOCKS
ARE OFTEN OMITTED
CORNER BLOCK
Figure 425. — Typical Rib Attachment to IBeam.
CORNER BLOCK EXERT5
PRESSURE AGAINST BOTH
THE BEAM AND THE RIB
VERTICAL MEMBER
\i_ MEMBER 15 GLUED
TO THE BEAM BEFORE RIB ATTACHMENT
TO ACT A5 A LOCATING FIXTURE
Figure 426. — Use of Rib Vertical as Locating Fixture.
220
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
The end rib verticals of plywood web type ribs are sometimes preassembled to
plain rectangular spars to act as locating members for ribtospar assembly. This is
shown in figure 426. Preassembled locating corner blocks might also be used to ad
vantage in other types of ribtospar attachments if care is taken to provide sufficient
backing for plywood webs to which corner blocks are being glued so that sufficient gluing
pressure can be obtained.
Canted ribs may be attached to beam members by beveling the ends of the ribs
or by using corner blocks as shown in figure 427.
Figure 427. — Typical Canted Rib to Spar Attachment
4.4. FRAMES AND BULKHEADS.
4.40 Types of Frames and Bulkheads. No one type of frame or bulkhead seems
to be the best for all types of loading, but the laminated ring is probably the best type
for use as an intermediate stiffening frame. Frames or bulkheads are usually made of
formed laminated wood, cut or routed from plywood, or are a combination of the two
(fig. 428).
4.41. Glue Area for Attachment of Plywood Covering. Care must be taken when
using the routed plywood type of bulkhead that the plywood edge provides sufficient
gluing area for the skin. It is often necessary to glue solid wood to the face of the ring
near its edge to provide additional gluing surface. This is illustrated in figure 429.
4.42. Reinforcements for Concentrated Loads. When concentrated loads are car
ried into a frame it may be desirable to scarf in some highdensity material and brace
the frame with a plywood web or solid truss members.
4.5. STIFFENERS.
4.50. General. The terms "stringer," "stiffener," and "intercostal" are often used
interchangeably. In the following discussion, "stringer" will refer to members con
tinuous through ribs and frames and "intercostal" will refer to members terminating
at each rib or frame. The term "stiffener" will not be used, since both stringers and
intercostals act as stiffeners.
DETAIL STRUCTURAL DESIGN
Section AA
Figure 429. — Use of Glue Blocks with Routed Plywood Bulkhead.
222
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
4.51. Attachment of Stringers. Ribs or frames must be notched if stringers are
used. A method of reinforcing these notches and fastening the stringers to the rib or
frame is illustrated in figure 430. Attachments may also be made by one of the methods
shown in figure 434.
A'i
 R»inf oreenant 
Figure 430. — Stringer Through Frame Joint.
4.52. Attachment of Intercostals. All intercostals should be firmly attached to
ribs or frames. Figure 431 illustrates the undesirable practice of terminating inter
costals some distance from the rib or frame. This usually results in cleavage along the
glue line starting at the free end of the intercostal. It is better to butt the stiffeners to
the rib or frame and fasten them with saddle gussets as illustrated in figure 432 or by
one of the attachments shown in figure 434.
Figure 431. — Poor Method of Intercostal Attachment.
Figure 432. — Acceptable Method of Intercostal Attachment.
4.6. GLUE JOINTS.
4.60. General. Glue joints should be used for all attachments of wood to wood
unless concentrated loads, cleavage loads, or other considerations necessitate the use
of mechanical connections.
4.61. Eccentricities. Eccentricities and tension components should be avoided in
glue joints by means of careful design. Figure 433 illustrates an example of an eccen
tricity and a method of avoiding it.
DETAIL STRUCTURAL DESIGN
223
Skin
Frame
1
. — Frame should be thick enough
to keep stresses In the glue
♦P line low.
Plywood Gusset. An alternate
method is to carry an inside
skin to the next frame, form
ing a symmetrical box structure.
Figure 433. — Joint in a Shell Structure.
4.62. Avoidance of End Grain Joints. End grain glue joints will carry no appre
ciable load. Strength is given to such a joint by using corner blocks or gussets as shown
in figure 434. These sketches are typical of joints encountered in joining rib members,
in attaching ribs to beams or intercostals to frames, or any other similar application.
Square
Triangular
Corner Blocks
Quarter Round
lywood gusset should
lap far enough so that
the gl ue area is suf
ficient to keep the
stresses low.
Plywood Angle Plywood Gusset
Figure 434. — Typical Reinforcement of End Grain Joints.
224
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
4.63. Gluing of Plywood over WoodPlywood Combinations. Many secondary
glue joints must be made between plywood covering and woodplywood structural mem
bers having plywood edges appearing on the surface to be glued. Woodplywood beams
or wing ribs employing continuous gussets are examples of such members. The plywood
edge has a tendency to project above the surface thereby preventing contact between
the plywood covering and the wood portion of the woodplywood surface. This condition
can be the result of differential shrinkage between the wood and plywood or may be
caused by the surfacing machine having a different effect cutting across the grain of the
plywood from cutting parallel to the grain of the wood. Figure 435 shows this condition
and shows how it can be eliminated by beveling the edges of the plywood.
Figure 435. — Beveling of Plywood Webs and Gussets.
4.64. Gluing of HighDensity Material. Better glue joints can be obtained be
tween a highdensity material and a relatively soft wood if the surface of the high
density material is sanded before gluing. The purpose of sanding is to remove the glazed
surface present on highdensity material and present on some plywoods. Satisfactory
compregtocompreg joints can be made if both surfaces are machined perfectly flat
immediately prior to gluing.
4.7. MECHANICAL JOINTS.
4.70. General. Mechanical Joints in wood are usually limited to types employing
aircraft bolts. Since bolts in wood can carry a much higher load parallel to the grain
of the wood than across the grain, it is generally advantageous to design a fitting and its
mating wood parts so that the loads on the bolts are parallel to the grain. The use of a
pair of bolts on the same grain line, carrying loads perpendicular to the grain and oppo
sitely directed, is likely to increase the tendency to split. When a long row of bolts is
used to join two parts of a structure, consideration should be given to the relative de
formation of the parts, as explained in section 4.82.
4.71. Use of Bushings. Bushings are often used in wood to provide additional
bearing area and to prevent crushing of the wood when bolts are tightened (fig. 436).
When bolts of large L/D (length/diameter) ratio are used, or when bolts are used through
a member having highdensity plates on the faces, plug bushings may be used to advantage.
4.72. Use of HighDensity Material. Wherever highly concentrated loads are in
troduced, greater bearing strength can be obtained by scarfingin highdensity material
(sec. 4.63). Some high density materials are quite sensitive to stress concentrations and
the possibility of the serious effects of such stress concentrations should be considered
when large loads must be carried through the highdensity material.
DETAIL STRUCTURAL DESIGN
225
Through bushing made
slightly shorter than
the width of the beam.
Throurh Bushing
Plug Bushing
Figure 436. — Types of Bushings.
Wherever metal fittings are attached to wood members, it is generally advisable to
reinforce the wood against crushing by the use of highdensity bearing plates (fig. 437),
and to use a coat of bitumastic or similar material between the wood and metal to guard
against corrosion. Cross banding of these plates will help to prevent splitting of the solid
wood member.
1 1 : ' 1
if
i i — r
i — r
l — r
■OfiBBS
High Density
Material
Metal Fitting
Cross Banded Filler Block
Figure 437. — Typical Wing Beam Attachment.
226
ANC BULLETIN
— DESIGN OF
WOOD AIRCRAFT STRUCTURES
HIGH DENSITY
BEARING PLATE
Fioure 438. — Distribution of Crushing Loads.
4.7 3. Mechanical Attachment of Ribs. When ribs carry heavy or concentrated
loads it is sometimes desirable to insure their attachment by use of mechanical fastenings
(fig. 439).
TO
TO THE! SPAR BY MEAN5 OF TO THE. SPAR BY MEAN5 OF
METAL ANGLES. METAL CLIPS
Figure 439. — Mechanical Attachment of Ribs.
4.74. Attachment of Various Types of Fittings. Fittings should have wide base
plates to prevent crushing at edges. Wood washers have a tendency to cone under tight
ening loads. Where possible, it is desirable to use washer plates for bolt groups, as illus
trated in figure 440, but if washers are used, a special type for wood, AN970 or equiva
lent, are necessary to provide sufficient bearing area.
Clamps around wood members should be constructed so that they can be tightened
symmetrically (fig. 441). ,
4.7 5. Use of Wood Screws, Rivets, Nails, and SelfLocking Nuts. Wood screws
and rivets are sometimes used for the attachment of secondary structure but should not
be used in connecting primary members. Wood screws have been successfully used to
prevent cleavage of plywood skin from stringers in some skinstringer applications.
Nails should never be used in aircraft to carry structural loads.
Selflocking nuts of approved types designed for use with wood and plywood
structures are preferable to plate or anchor nuts. When the latter type is used, however,
attachment may be made to the structure with wood screws or rivets provided that
care is taken not to reduce the strength of loadcarrying members. Riveting through
wood is always questionable because of the danger of crushing the wood under the rivet
heads and the possibility of bending the shank while bucking the rivet. Also, there is
DETAIL STRUCTURAL DESIGN
227
Figure 441. — Installation of Clamp Fittings.
no way of tightening the joint when dimensional changes from shrinkage occur.
4.8. MISCELLANEOUS DESIGN DETAILS.
4.80. Metal to Wood Connections. Metal to wood connections are complicated
by an inherent weakness of all untreated wood— low shear and bearing strength. Sec
tions 4.6 and 4.7 present various methods of minimizing this drawback.
Another way of improving the efficiency of wood structures is to keep the number
of joints to a minimum. For example, when other design considerations will permit, a
onepiece wood wing is desirable; when this is not permissible, the wing joint should be
placed as far outboard as possible so that the fitting loads will be low.
4.81. Stress Concentrations. Since wood in tension has practically no elongation
between the proportional limit and the ultimate strength, there is little of the "internal
adjustment" common to metal structures. Stress concentrations, therefore, become
more critical and, for efficient design, must be held to a minimum. The fact that com
preg and similar materials are very sensitive to stress concentrations should be carefully
considered when these materials are used.
228
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
4.82. Behavior of Dissimilar Materials Working Together. When materials of
differing rigidities, such as normal wood, compreg, or metal fittings, are fastened to
gether for a considerable distance and are under high stress, consideration should be
given to the fact that the fastening causes the total deformation of all materials to be the
same. A typical example is a long metal strap bolted to a wood spar flange for the pur
pose of taking the load out of the wood at a wing joint. In order that the load be uni
formly distributed among the bolts, the ratio of the stress to the modulus of elasticity
should be the same for both materials at every point. This may be approximated in
practical structures by tapering the straps and the wood in such a manner that the
average stress in each (over the length of the fastening) divided by its modulus of
elasticity gives the same ratio.
When splicing highdensity materials to wood, or in dropping off bearing plates,
the slope of the scarf should be less steep than the slope allowed for normal wood.
4.83. Effects of Shrinkage. When the moisture content of a piece of wood is
lowered its dimensions decrease. The dimensional change is greatest in a tangential
direction (across the fibers and parallel to the growth rings), somewhat less in a radial
direction (across the fibers and perpendicular to the growth rings), and is negligible in a
longitudinal direction (parallel to the fibers). For this reason a flatgrained board will
have a greater change in width for a given moisture content change than an edge
grained board. Flatgrained boards also have a greater tendency to warp than do edge
grained boards.
These dimensional changes can have several deleterious effects upon a wood structure
and the designer must study each case to determine which effects are most harmful,
and which are the most satisfactory methods of minimizing them. Loosening of fittings
and wire bracing are common results of shrinkage. Checking or splitting of wood
members frequently occurs when shrinkage takes place in members that are restrained
against dimensional change. Restraint is sometimes given by metal fittings and quite
often by plywood reinforcements since plywood shrinkage is roughly only 1/20 of cross
grain shrinkage of solid wood.
A few of the methods of minimizing these shrinkage effects are:
1. Use bushings that are slightly short so that when the wood member shrinks
the bushings do not protrude and the fittings may be tightened firmly against the
member (fig. 436).
2. Place the wood so that the more important face, in regard to maintaining dimen
sion, is edgegrained. For example, solid spars are required to be edgegrained on their
vertical face so that the change in depth is a minimum.
Figure 442. — Protection Against Splitting.
I
DETAIL STRUCTURAL DESIGN 229
3. Wood members can be reinforced against checking or splitting by means of
plywood inserts or cross bolts (fig. 442). Care should be taken to avoid constructions
that introduce cleavage (crossgrain) loads when shrinkage occurs.
4. Plywood face plates should be dropped off gradually either by feathering or
by shaping so that the cleavage loads at the edge of the plywood are minimized when
shrinkage occurs (fig. 443).
fEATHERED END7 SPADED END 7
4.84. Drainage and Ventilation. Wood structures must be adequately drained
to insure a normal length of service life. This applies to box spar sections as well as all
low portions of wings and fuselages. The usual method is to drain each compartment
separately as illustrated in figure 444. Another acceptable method is to drain from
one compartment to another until the lowest compartment is reached, or structural
requirements prohibit further internal drainage, before drainage holes to the exterior
are bored. This method is illustrated in figure 445.
:l/4 inch holes drilled at the
low points of all compartments
Figure 444. — Drainage Diagram of Wing, Direct Method.
Service experience indicates that drainage holes for individual compartments
should be not less than onequarter inch in diameter, with threeeighths inch being
preferable. Drainage holes to the exterior used with the internal drainage system should
probably be somewhat larger. If the internal drainage system is used it is suggested
230 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
A A 1/2 inch holes drilled at the low
point of the lowest compartments 
Figure 445. — Drainage Diagram of Wing, Internal Method.
that the intercompartment drainage holes be inspected after the internal finish has
been applied to make sure that the finish has not clogged the internal drain holes. This
will necessitate attaching the top skin last.
Drain holes are usually drilled from the external surface so that the splintering
does not mar the external finish. After drilling drain holes, all splinters should be care
fully removed from the inner surface, and the edges of the holes should be sanded
lightly and protected by the application of several coats of spar varnish. It is common
practice, in order to avoid damage to structural members by the drill, to drill drainage
holes an appreciable distance from the low corner of a compartment. This practice
must be avoided and some method of insuring proper location of drain holes at the
actual low points must be developed by the aircraft manufacturer that will not only
prevent damage to the framework but will also provide complete drainage of the
structure.
It is, therefore, recommended that proof of the adequacy of the drainage system
chosen be demonstrated by setting up the structure, with the top cover removed, in a
position corresponding to its attitude when the airplane is resting on the ground. Water
is then poured into the structure and the actual performance of the drainage system
observed.
Careful design to prevent entry of water into the structure is equally important.
Careful location of all openings and use of boots and gaskets should be considered. If
interiors do happen to get wet, good ventilation will accelerate the drying. Marine
grommets have been suggested for use with external drain holes in wing, tail, and control
surfaces. This type of grommet produces a suction or scavenging action in flight and
also protects the holes themselves from direct splash during taxiing on wet or muddy
fields. Periodic inspection and cleaning of drainage holes covered with marine grommets,
however, may be difficult.
4.8 5. Internal Finishing. It is recognized that applying finish to the inner surfaces
DETAIL STRUCTURAL DESIGN
231
of the closing panels of plywoodcovered structures is a difficult problem. The usual
method, other than dipping, is to mask off the locations of secondary glue areas prior
to the application of finish to the surface, for wood coated with a protective finish can
not be glued. This is a timeconsuming operation, and after the plywood covering is
finally fitted into place, the film of finish usually stops short of the intersection lines
between the plywood covering and framework. These are the very places where the
finish is needed most if water does accumulate in the interior.
Woodrotting organisms can act only if the moisture content of the wood is above
approximately 20 to 25 percent. Although finishes will not prevent moisture content
changes in wood, they will retard such changes so that the wood moisture content will
not follow the rapid changes in atmospheric conditions but only the more gradual
changes. Therefore, if wood members are finished, dangerously high moisture contents
will be reached in wood aircraft structures only when parts are in contact with standing
water since atmospheric conditions that produce high moisture contents are generally
of relatively short duration, except in extreme climates such as the tropics, and the
retarding effect of the finish may be expected to prevent the wood from attaining a
high moisture content within this short period.
In view of the foregoing discussion, it is suggested that consideration be given to
the following method of finishing the inner surfaces of plywoodcovered assemblies.
Since any free water would be in contact with the lower skin almost entirely, the lower
wing covering and control surface coverings should be attached to the framework prior
to the upper covering. In this way, finish can be applied thoroughly to the lower cover
ing and adjacent framework quite easily after the assembly gluing operation has been
completed. Since gaps in the finish on the upper covering along framework members
are not so harmful as they would be on the inner surfaces of the lower covering, wider
masking strips may be used over secondary glue areas on the upper covering at the time
of applying the internal finish, thereby reducing the chance of finished surfaces falling
over framework members. Some method of accurately registering the covering should
be used.
4.86. External Finishing. Two types of external finish for plywood covered air
craft have been used successfully, the directtoplywood finish and the fabriccovered
plywood finish. There is little difference in weight between the two systems because
the weight of the fabric is offset by the difference in weight between the finishes used
in the two systems.
Directtoplywood finishes have a tendency to check wherever a glue joint appears
on the surface. Checking of the finish is also apt to occur when the grain of the wood
tends to raise, as in those softwoods having appreciable contrast between spring and
summerwood, such as Douglasfir. Fabriccovered finishes do not check from these
causes.
Light airplane fabric of the type specified in ANC83 is the usual material used
for the fabriccovered plywood finish system. The fabric provides a better protection
from the abrasive action of stones, sand, and other objects kicked up while taxiing
than does the directtoplywood finish.
Observation of wood airplanes in service has revealed that plywood or fiber plates
glued over exposed end grain may act as a moisture trap rather than as a moisture
barrier. Several coats of brushedin aluminized spar varnish are believed to give a much
232
ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
more satisfactory protection to exposed end grain. Exposed end grain should be
interpreted to include exposed feathered surfaces.
4.87. Selection of Species. Properties other than the usually listed strength and
elastic properties should also be considered when selecting a wood for any specific
purpose. For example, birch and maple are relatively difficult to glue; yellowpoplar
has lower resistance to shock than spruce; Douglasfir is low in cleavage strength.
4.88. Use of Standard Plywood. From a maintenance viewpoint it is desirable
FUSELAGE PANEL
FUSELAGE NOSE SECTION
Figure 446. — Fuselage Framework.
DETAIL STRUCTURAL DESIGN 233
to use only standard plywoods for design so that too great a variety of types will not
need to be carried in stock. Table 2 9 lists many of the more common constructions.
If one of these is used, the formulas in chapter 2 can be used with greater ease because
many of the basic parameters and strength values are given in this table. Twoply
diagonal plywood is considered a special construction by most plywood manufacturers
and has the disadvantage of tending to warp because of its unsymmetrical construction.
4.89. Tests. Quite often, time and effort may be saved by the use of simple tests
in the early stages of the design of complex joints.
4.9. EXAMPLES OF ACTUAL DESIGN DETAILS.
On the following pages several sketches and photographs are presented to show
how various manufacturers have treated details encountered in the design of wood
aircraft. No effort has been made to label these sketches as either good or poor practice.
They are merely presented to show what the industry has done when confronted with
specific problems (figs. 446 through 463).
234
ANC BULLETIN— DESTGN OF WOOD AIRCRAFT STRUCTURES
?0UTED SPRUCE
 MAHOGANY POPLAR
PLYWOOD
DRAINAGE AND VENTILATION 1
HOLES
FIN BEAM
WALNUT POPLAR —
PLYWOOD PLATE5
AIRPLANE
WING BEAM
SHOWING BLOCKING AND PLATING AT LOCATION
OF APPLICATION OF CONCENTRATED LOAD5
Figure 447. — Examples of Beams.
DETAIL STRUCTURAL DESIGN
235
End Doaljrn.
Th« following changes from the
orlglaaJ. design were Incorpora
ted.
1. Bearing bloolta Item 1 removed.
2. Faoo plat© item 6 added.
S. find aeotlon of item 3 outout
and apruoe wedges Item 6 in
stalled with.jgreln porpindi
oular to thfj spir axi o .
Failure ooourrai to indicated «
B,  10,100 f
U.  7600 #
BJ1  183,063 in. lb*.
3rd Design.
The following ohengea from the
2nd design were incorporated .
1* Tertioel grain ipruoe wedges
Item 6 eliminated.
2. Hotel straps added*
3. Bolt and bearing plates added*
Loaded tot
B, «= 21,400
Hp «' 16,100
B.H  367,676 in. lbs*
without failure.
HITERIAL BOTES
@ J" Mapl*
(7^ 1/8" 3 Ply Mahogany
(Tlj 1" Spruoe
(T^ i" 46° 4 Ply Mahogany
fs«) 4 Ply Mahogany
^— ^ (Faoe Grain Parallel to Spar Axis)
(7l) Sprue* * (Grain Perpandloula* to Spar Axis)
Figure 448.— Cantilever Wood Spar at Fuselage Attachment.
DETAIL STRUCTURAL DESIGN
237
Figure 450.— Spar Details at Root Section and Fuselage Attachment.
238
ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
Figure 451. — Further Spar Details at Root Section and Fuselage Attachment.
DETAIL STRUCTURAL DESIGN
230
Figure 454. — Method of Double Drag Bracing.
DETAIL STRUCTURAL DESIGN
241
Figure 455. — Attachment of Flap Hinge.
242
ANC BULLETIN — DESIGN OP WOOD AIRCRAFT STRUCTURES
Figure 456. — Attachment of Empennage.
DETAIL STRUCTURAL DESIGN
243
<m **** 1
9 PLY
mah  po plar
1 Ply w o
S,TCA/0/V F ~ F
Figure 457. — Reinforced Fuselage Frame.
244 ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES
DETAIL STRUCTURAL DESIGN
245
r— METAL TORQUE. TUBE
Figure 460. — Example of Elevator Torque Tube Attachment to Control Surface.
246 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES
MUST BE. FLUSH (FIRLWALL INSTALLATION)
Figure 462. — Typical Fuselage Joint or Engine Mount Attachment.
I
I
MEMORANDUM
1
MEMORANDUM
■
MEMORANDUM
MEMORANDUM